Dissertationen zum Thema „Predictive programming“

Avhandling för teknologie doktorsexamen i datavetenskap, som kommer att försvaras offentligt tisdagen den 11 mars 2014 kl. 13.15, M404, Högskolan i Borås. Opponent: docent Niklas Lavesson, Blekinge Tekniska Högskola, Karlskrona.

This thesis develops efficient optimization methods for Model Predictive Control (MPC) to enable its application to constrained systems with fast and uncertain dynamics. The key contribution is an active set method which exploits the parametric nature of the sequential optimization problem and is obtained from a dynamic programming formulation of the MPC problem. This method is first applied to the nominal linear MPC problem and is successively extended to linear systems with additive uncertainty and input constraints or state/input constraints. The thesis discusses both offline (projection-based) and online (active set) methods for the solution of controllability problems for linear systems with additive uncertainty. The active set method uses first-order necessary conditions for optimality to construct parametric programming regions for a particular given active set locally along a line of search in the space of feasible initial conditions. Along this line of search the homotopy of optimal solutions is exploited: a known solution at some given plant state is continuously deformed into the solution at the actual measured current plant state by performing the required active set changes whenever a boundary of a parametric programming region is crossed during the line search operation. The sequence of solutions for the finite horizon optimal control problem is therefore obtained locally for the given plant state. This method overcomes the main limitation of parametric programming methods that have been applied in the MPC context which usually require the offline precomputation of all possible regions. In contrast to this the proposed approach is an online method with very low computational demands which efficiently exploits the parametric nature of the solution and returns exact local DP solutions. The final chapter of this thesis discusses an application of robust tube-based MPC to the nonlinear MPC problem based on successive linearization.

Platooning is an interesting area which involve the possibility of decreasing the fuel consumption of heavy-duty vehicles. By reducing the inter-vehicle spacing in the platoon we can reduce air drag, which in turn reduces fuel consumption. Two fuel-efficient model predictive controllers for HDVs in a platoon has been formulated in this master thesis, both utilizing road grade preview information. The first controller is based on linear programming (LP) algorithms and the second on quadratic programming (QP). These two platooning controllers are compared with each other and with generic controllers from Scania. The LP controller proved to be more fuel-efficient than the QP controller, the Scania controllers are however more fuel-efficient than the LP controller.

This thesis is concerned with different topics in multi-parametric programming and explicit model predictive control, with particular emphasis on hybrid systems. The main goal is to extend the applicability of these concepts to a wider range of problems of practical interest, and to propose algorithmic solutions to challenging problems such as constrained dynamic programming of hybrid linear systems and nonlinear explicit model predictive control. The concepts of multi-parametric programming and explicit model predictive control are presented in detail, and it is shown how the solution to explicit model predictive control may be efficiently computed using a combination of multi-parametric programming and dynamic programming. A novel algorithm for constrained dynamic programming of mixed-integer linear problems is proposed and illustrated with a numerical example that arises in the context of inventory scheduling. Based on the developments on constrained dynamic programming of mixed-integer linear problems, an algorithm for explicit model predictive control of hybrid systems with linear cost function is presented. This method is further extended to the design of robust explicit controllers for hybrid linear systems for the case when uncertainty is present in the model. The final part of the thesis is concerned with developments in nonlinear explicit model predictive control. By using suitable model reduction techniques, the model captures the essential nonlinear dynamics of the system, while the achieved reduction in dimensionality allows the use of nonlinear multi-parametric programming methods.

This thesis describes a novel technique for learning predictive models from nondeterministic spatio-temporal data. The prediction models are represented as a production system, which requires two parts: a set of production rules, and a conflict resolver. The production rules model different, typically independent, aspects of the spatio-temporal data. The conflict resolver is used to decide which sub-set of enabled production rules should be fired to produce a prediction. The conflict resolver in this thesis can probabilistically decide which set of production rules to fire, and allows the system to predict in non-deterministic situations. The predictive models are learnt by a novel technique called Spatio-Temporal Genetic Programming (STGP). STGP has been compared against the following methods: an Inductive Logic Programming system (Progol), Stochastic Logic Programs, Neural Networks, Bayesian Networks and C4.5, on learning the rules of card games, and predicting a person’s course through a network of CCTV cameras. This thesis also describes the incorporation of qualitative temporal relations within these methods. Allen’s intervals [1], plus a set of four novel temporal state relations, which relate temporal intervals to the current time are used. The methods are evaluated on the card game Uno, and predicting a person’s course through a network of CCTV cameras. This work is then extended to allow the methods to use qualitative spatial relations. The methods are evaluated on predicting a person’s course through a network of CCTV cameras, aircraft turnarounds, and the game of Tic Tac Toe. Finally, an adaptive bloat control method is shown. This looks at adapting the amount of bloat control used during a run of STGP, based on the ratio of the fitness of the current best predictive model to the initial fitness of the best predictive model.

The situation when driving in dense traffic and at low speeds is called Stop and Go. A controller for automatic following of the car in front could under these conditions reduce the driver's workload and keep a safety distance to the preceding vehicle through different choices of gear and engine torque. The aim of this thesis is to develop such a controller, with an additional focus on lowering the fuel consumption. With help of GPS, 3D-maps and sensors information about the slope of the road and the preceding vehicle can be obtained. Using this information the controller is able to predict future possible control actions and an optimization algorithm can then find the best inputs with respect to some criteria. The control method used is Model Predictive Control (MPC) and as the name indicate a model of the control object is required for the prediction. To find the optimal sequence of inputs, the optimization method Dynamic Programming choose the one which lead to the lowest fuel consumption and satisfactory following. Simulations have been made using a reference trajectory which was measured in a real traffic jam. The simulations show that it is possible to follow the preceding vehicle in a good way and at the same time reduce the fuel consumption with approximately 3 %.

The system for mission handling in the Gripen fighter aircraft, and in its ground supporting system, consists for example of ways to plan mission routes, create mission points and validate performed missions. The system is complex and for example, the number of different mission points used increases due to changing demands and needs. This master thesis presents suggestions for improvements and simplifications for the mission handling system, to make it more intuitive and more friendly to use. As a base for the suggestions, interviews with pilots from Saab, TUJAS and FMV have been conducted, this is to obtain opinions and ideas from those using the system and have deep knowledge about it. Another possible assistance and improvement is to provide the possibility of on-line automatic re-planning of the mission route in case of obstacles. MPC (Model Predictive Control) has been used to estimate the obstacle’s flight path,and calculate a new route to the next mission point which does not conflict with the estimated enemy’s path. This system has been implemented in Matlab and the concept is demonstrated with different test scenarios where the design parameters (prediction horizon and penalty in the cost function) for the controller are varied, and stationary and moving obstacles are induced.
Systemet för uppdragshantering i stridsflygplanet Gripen, och i dess markstödsystem, består bland annat av uppdragsplanering, skapande av uppdragspunkter och möjligheter att validera utförda uppdrag. Systemet är komplext och exempelvis växer antalet uppdragspunkter med omvärldens ökande krav och behov. Detta examensarbete presenterar förslag till förenklingar och förbättringar i uppdragshanteringssystemet, för att göra det mer intuitivt och användarvänligt. Som grund för förslagen har intervjuer med piloter från Saab, TUJAS och FMV gjorts, för att samla in åsikter och idéer från de som använder systemet och har bred kunskap om det. En förbättring är en möjlighet till online automatisk omplanering av uppdragsrutten vid hinder. MPC (modellbaserad prediktionsreglering) har använts för att estimera den dynamiska fiendens flygväg, och beräkna en ny rutt till nästa uppdragspunkt som inte ligger i konflikt med den estimerade vägen för hindret. Detta system har implementerats i Matlab och konceptet demonstreras med olika testscenarion där prestandaparametrar (prediktionshorisont och straff i kostnadsfunktionen) för regulatorn varieras, och stationära och rörliga hinder induceras.

This thesis presents a predictive energy management controller for long-haul hybrid trucks. In a receding horizon control framework, the vehicle speed reference, battery energy reference, and engine on/off decision are optimized over a prediction horizon. A mixed-integer quadratic program (MIQP) is formulated by performing modelling approximations and by including the binary engine on/off decision in the optimal control problem. The branch-and-bound algorithm is applied to solve this problem. Simulation results show fuel consumption reductions between 10-15%, depending on driving cycle, compared to a conventional truck. The hybrid truck without the predictive control saves significantly less. Fuel consumption is reduced by 3-8% in this case. A sensitivity analysis studies the effects on branch-and-bound iterations and fuel consumption when varying parameters related to the binary engine on/off decision. In addition, it is shown that the control strategy can maintain a safe time gap to a leading vehicle. Also, the introduction of the battery temperature state makes it possible to approximately model the dynamic battery power limitations over the prediction horizon. The main contributions of the thesis are the MIQP control problem formulation, the strategy to solve this with the branch-and-bound method, and the sensitivity analysis.

The power to mass ratio of a heavy truck causes even moderate slopes to have a significant influence on the motion. The velocity will inevitable vary within an interval that is primarily determined by the ratio and the road topography. If further variations are actuated by a controller, there is a potential to lower the fuel consumption by taking the upcoming topography into account. This possibility is explored through theoretical and simulation studies as well as experiments in this work.

Look-ahead control is a predictive strategy that repeatedly solves an optimization problem online by means of a tailored dynamic programming algorithm. The scenario in this work is a drive mission for a heavy diesel truck where the route is known. It is assumed that there is road data on-board and that the current heading is known. A look-ahead controller is then developed to minimize fuel consumption and trip time.

The look-ahead control is realized and evaluated in a demonstrator vehicle and further studied in simulations. In the prototype demonstration, information about the road slope ahead is extracted from an on-board database in combination with a GPS unit. The algorithm calculates the optimal velocity trajectory online and feeds the conventional cruise controller with new set points. The results from the experiments and simulations confirm that look-ahead control reduces the fuel consumption without increasing the travel time. Also, the number of gear shifts is reduced. Drivers and passengers that have participated in tests and demonstrations have perceived the vehicle behavior as comfortable and natural.

Report code: LIU-TEK-LIC-2007:28.

New and exciting possibilities in vehicle control are revealed by the consideration of topography through the combination GPS and three dimensional road maps. This thesis explores how information about future road slopes can be utilized in a heavy truck with the aim at reducing the fuel consumption over a route without increasing the total travel time.

A model predictive control (MPC) scheme is used to control the longitudinal behavior of the vehicle, which entails determining accelerator and brake levels and also which gear to engage. The optimization is accomplished through discrete dynamic programming. A cost function is used to define the optimization criterion. Through the function parameters the user is enabled to decide how fuel use, negative deviations from the reference velocity, velocity changes, gear shifts and brake use are weighed.

Computer simulations with a load of 40 metric tons shows that the fuel consumption can be reduced with 2.5% with a negligible change in travel time, going from Link¨oping to J¨onk¨oping and back. The road slopes are calculated by differentiation of authentic altitude measurements along this route. The complexity of the algorithm when achieving these results allows the simulations to run two to four times faster than real time on a standard PC, depending on the desired update frequency of the control signals.

A mini dissertation submitted to the Faculty Of Education in partial fulfillment of the requirements for the Degree Of Master Of Education (Research Methodology) in the Department of Educational Psychology and Special Needs Education at the University Of Zululand, 2017
Introduction to Programming Systems is considered to be very difficult and has a very high average failure rate of between 30% and 40%. Some researchers have studied the characteristics of students who pass Introduction to Programming Systems without struggling and used those characteristics as predictors of success in Introduction to Programming Systems. This research studied the relationship between selected predictors (Calculus, Discrete Mathematics, Classic Mechanics and General Chemistry) and Introduction to Programming Systems. The study adapted a case study and correlation research design. A sample size of 399 was selected using a non-probability sampling method called convenient sampling. Data from only one university were used. SPSS’s Pearson correlation and multiple regression was used to analyse the collected data. The results showed that there is a positive correlation between the criterion (Introduction to Programming Systems) and the predictors. Multiple regression results showed that the ordinal strength of predictor was as follows: Calculus, Discrete Mathematics, Classic Mechanics and General Chemistry. Only General Chemistry had an insignificant effect on the criterion. The variation was 34 %.

The main topic of this thesis is integer quadratic programming with applications to problems arising in the areas of automatic control and communication. One of the most widespread modern control methods is Model Predictive Control (MPC). In each sampling time, MPC requires the solution of a Quadratic Programming (QP) problem. To be able to use MPC for large systems, and at high sampling rates, optimization routines tailored for MPC are used. In recent years, the range of application of MPC has been extended to so-called hybrid systems. Hybrid systems are systems where continuous dynamics interact with logic. When this extension is made, binary variables are introduced in the problem. As a consequence, the QP problem has to be replaced by a far more challenging Mixed Integer Quadratic Programming (MIQP) problem, which is known to have a computational complexity which grows exponentially in the number of binary optimization variables. In modern communication systems, multiple users share a so-called multi-access channel. To estimate the information originally sent, a maximum likelihood problem involving binary variables can be solved. The process of simultaneously estimating the information sent by multiple users is called Multiuser Detection (MUD). In this thesis, the problem to efficiently solve MIQP problems originating from MPC and MUD is addressed. Four different algorithms are presented. First, a polynomial complexity preprocessing algorithm for binary quadratic programming problems is presented. By using the algorithm, some, or all, binary variables can be computed efficiently already in the preprocessing phase. In numerical experiments, the algorithm is applied to unconstrained MPC problems with a mixture of real valued and binary valued control signals, and the result shows that the performance gain can be significant compared to solving the problem using branch and bound. The preprocessing algorithm has also been applied to the MUD problem, where simulations have shown that the bit error rate can be significantly reduced compared to using common suboptimal algorithms. Second, an MIQP algorithm tailored for MPC is presented. The algorithm uses a branch and bound method where the relaxed node problems are solved by a dual active set QP algorithm. In this QP algorithm, the KKT systems are solved using Riccati recursions in order to decrease the computational complexity. Simulation results show that both the proposed QP solver and MIQP solver have lower computational complexity compared to corresponding generic solvers. Third, the dual active set QP algorithm is enhanced using ideas from gradient projection methods. The performance of this enhanced algorithm is shown to be comparable with the existing commercial state-of-the-art QP solver \cplex for some random linear MPC problems. Fourth, an algorithm for efficient computation of the search directions in an SDP solver for a proposed alternative SDP relaxation applicable to MPC problems with binary control signals is presented. The SDP relaxation considered has the potential to give a tighter lower bound on the optimal objective function value compared to the QP relaxation that is traditionally used in branch and bound for these problems, and its computational performance is better than the ordinary SDP relaxation for the problem. Furthermore, the tightness of the different relaxations is investigated both theoretically and in numerical experiments.
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The freight transport has a fundamental role in the world’s economic development.Due to the flexibility of heavy-duty vehicles, a large part of freighttransport is carried out inland. Although the use of heavy-duty vehicles contributesto the economic growth, the increased fuel consumption and globalgreenhouse gas emission that come with it constantly challenge the transportationsector to adapt and develop more fuel-efficient methods to reduce suchside effects while fulfilling the transportation requirements.This thesis considers fuel-optimal highway driving for heavy-duty vehicles.A model predictive control algorithm for minimizing fuel consumptionwhile satisfying constraints on desired speed is developed and evaluated. Thecontroller uses the available topography information of the road ahead of thevehicle in order to achieve an efficient vehicle control while satisfying a certaintrip time requirement. Under the assumption of fixed gear during the drivemission, the actual nonlinear problem is re-formulated as a real-time optimalcontrol problem based on MPC theory with a quadratic cost function and linearconstraints at each receding horizon of the drive mission. The QP problem isthen solved online and the resulting first control action is applied to the vehiclefor forward movement.The feasibility to implement such an algorithm on a control unit with limitedcomputational power is investigated and shown to be possible. Both therequirement of low computational complexity and low memory occupation arefulfilled by the tailored quadratic programming algorithm developed in thisthesis. The algorithm is fast enough to provide a solution within each samplinginterval.The overall control algorithm is implemented on a G5 control unit andtested in real life with a Scania truck during highway driving test. The resultsfrom both the real implementation and extensive simulations indicate that themethod provides a fuel-efficient vehicle behavior and is competitive with a rulebasedcontroller.
Transport av gods har en grundläggande roll i världens ekonomiska utveckling.På grund av flexibiliteten hos tunga fordon, utförs en stor del av allgodstransport med hjälp av dem. Trots att användning av tunga fordon bidrartill ekonomisk tillväxt, utgör bränsleförbrukning tillsammans med den ökadeutsläpp av växthusgas en utmaning för transportföretag att anpassa och utvecklamer bränslesnål och miljövänligare transportteknologi för tunga fordon.I detta examensarbete fokuserar man på körningen av lastbil på motorvägar.En bränsle optimal förutsägande styralgoritm är utvecklad och utvärderad.Algoritmen utnyttjar framför allt topografi information om vägen framför fordonetså att den kan planera körningen på ett bränslesparande sätt samtidigtsom den uppfyller ett visst tidskrav. Med antagande om konstant växel underkörningen, formuleras ett optimal styrningsproblem baserat på ett MPC ramverkmed kvadratisk målfunktion och linjära bivillkor. Den slutliga kvadratiskoptimeringsproblemet för varje styrhorisont är löst med hjälp av en för ändamåletframtagen QP-algoritm.Möjligheten att implementera en sådan algoritm på en inbyggd styrenhetär undersökt och veriferad. Både krav på låg beräkningskomplexitet och lågminnes användning är uppfylls av den MPC-anpassade QP-lösare som utvecklatsi detta examensarbete.Den slutliga styralgoritmen testades i verkligheten med en Scania lastbilpå motorväg. Resultat från både provkörning och simulering visar att metodenger en bränsleeffektiv körstrategi, som kan spara bränsle jämfört med en regelbaseradprediktiv farthållaren.

A generic plant-wide control structure is proposed for the optimal operation of a grinding mill circuit. An economic objective function is defined for the grinding mill circuit with reference to the economic objective of the larger mineral processing plant. A mineral processing plant in this study consists of a comminution and a separation circuit and excludes the extractive metallurgy at a metal refinery. The comminution circuit's operational performance primarily depends on the mill's performance. Since grindcurves define the operational performance range of a mill, the grindcurves are used to define the setpoints for the economic controlled variables for optimal steady-state operation. For a given metal price, processing cost, and transportation cost, the proposed structure can be used to define the optimal operating region of a grinding mill circuit for the best economic return of the mineral processing plant. The plant-wide control structure identifies the controlled and manipulated variables to ensure the grinding mill circuit can be maintained at the desired operating condition. The plant-wide control framework specifies regulatory and supervisory control aims which can be achieved by means of non-linear model-based control. An impediment to implementing model-based control is the computational expense to solve the non-linear optimisation function. To resolve this issue, the reference-command tracking version of model predictive static programming (MPSP) is applied to a grinding mill circuit. MPSP is an innovative optimal control technique that combines the philosophies of Model Predictive Control (MPC) and approximate dynamic programming. The performance of the proposed MPSP control technique, is compared to the performance of a standard non-linear MPC (NMPC) technique applied to the same plant for the same conditions. Results show that the MPSP control technique is more than capable of tracking the desired set-point in the presence of model-plant mismatch, disturbances and measurement noise. The performance of MPSP and NMPC compare very well, with definite advantages offered by MPSP. The computational speed of MPSP is increased through a sequence of innovations such as the conversion of the dynamic optimization problem to a low-dimensional static optimization problem, the recursive computation of sensitivity matrices, and using a closed form expression to update the control. The MPSP technique generally takes only a couple of iterations to converge, even when input constraints are applied. Therefore, MPSP can be regarded as a potential candidate for on-line applications of the NMPC philosophy to real-world industrial process plants. The MPSP and NMPC simulation studies above assume full-state feedback. However, this is not always possible for industrial grinding mill circuits. Therefore, a non-linear observer model of a grinding mill is developed which distinguishes between the volumetric hold-up of water, solids, and the grinding media in the mill. Solids refer to all ore small enough to discharge through the end-discharge grate, and grinding media refers to the rocks and steel balls. The rocks are all ore too large to discharge from the mill. The observer model uses the accumulation rate of solids and the discharge rate as parameters. It is shown that with mill discharge flow-rate, discharge density, and volumetric hold-up measurements, the model states and parameters are linearly observable. Although instrumentation at the mill discharge is not yet included in industrial circuits because of space restrictions, this study motivates the benefits to be gained from including such instrumentation. An Extended Kalman Filter (EKF) is applied in simulation to estimate the model states and parameters from data generated by a grinding mill simulation model from literature. Results indicate that if sufficiently accurate measurements are available, especially at the discharge of the mill, it is possible to reliably estimate grinding media, solids and water hold-ups within the mill. Such an observer can be used as part of an advanced process control strategy.
'n Generiese aanlegwye beheerstruktuur vir die optimale beheer van 'n maalmeulkring word voorgehou. 'n Ekonomiese doelwitfunksie is gedefinieer vir die maalmeulkringbaan met verwysing tot die ekonomiese doelwit van die groter mineraalverwerkingsaanleg. 'n Mineraalverwerkingsaanleg bestaan in hierdie studie slegs uit die vergruisings- en skeidingskringbane. Die ekstraktiewe metallurgie by die metaal raffinadery word uitgesluit. Die vergruisingskringbaan se operasionele werksverrigting is hoofsaaklik van die maalmeul se werksverrigting afhanklik. Aangesien maalkurwes die bereik van die maalmeul se werksverrigting beskryf, kan die maalkurwes gebruik word om die stelpunte van die ekonomiese beheerveranderlikes te definieer vir werking by optimale gestadigde toestand. Gegewe 'n bepaalde metaalprys, bedryfskoste, en vervoerkoste, kan die voorgestelde struktuur gebruik word om die optimale werksgebied vir die maalmeulkring te definieer vir die beste ekonomiese gewin van die algehele mineraalverwerkingsaanleg. Die aanlegwye beheerstruktuur omskryf die beheerveranderlikes en manipuleerbare veranderlikes wat benodig word om die maalmeulkring by die gewenste werksgebied te handhaaf. Die aanlegwye beheerstruktuur spesifiseer regulatoriese en toesighoudende beheer doelwitte. Hierdie doelwitte kan bereik word deur gebruik te maak van nie-lineêre model gebaseerde beheer. Die probleem is dat die bewerkingskoste om nie-lineëre optimeringsfunksies op te los 'n struikelblok is om model gebaseerde beheer op industriële aanlegte toe te pas. Ter oplossing hiervan, word die stelpunt-volg weergawe van model gebaseerde voorspellende statiese programmering (MVSP) toegepas op 'n maalmeulkringbaan. MVSP is 'n innoverende optimale beheertegniek, en bestaan uit 'n kombinasie van die filosofieë van model gebaseerder voorspellende beheer (MVB) en aanpassende dinamiese programmering. Die verrigting van die voorgestelde MVSP beheertegniek word vergelyk met die verrigting van 'n standaard nie-lineëre MVB (NMVB) tegniek deur beide beheertegnieke op dieselfde aanleg vir dieselfde toestande toe te pas. Resultate dui aan dat die MVSP beheertegniek in staat is om die gekose stelpunt te midde van model-aanleg wanaanpassing, steurnisse, en metingsgeraas te volg. Die verrigting van MVSP en NMVB vergelyk goed, maar MVSP bied duidelike voordele. Die bewerkingspoed vir MVSP word vinniger gemaak deur die dinamiese optimeringsprobleem in 'n laeorde statiese optimeringsprobleem te omskep, die sensitiwiteitsmatrikse rekursief uit te werk, en deur 'n geslote uitdrukking ter opdatering van die beheeraksie te gebruik. Die MVSP beheertegniek benodig normaalweg slegs 'n paar iterasies om tot 'n oplossing te konvergeer, selfs indien beperkings op die insette toegepas word. Om die rede word MVSP as 'n potensiële kandidaat beskou vir aanlyntoepasings van die NMVB filosofie op industriële aanlegte. Die MVSP en NMVB simulasie studies hierbo neem aan dat volle toestandterugvoer moontlik is. Hierdie is nie altyd moontlik vir industriële maalmeulkringbane nie. Om die rede is 'n nie-lineêre waarnemingsmodel van 'n maalmeul ontwikkel. Die model onderskei tussen die volumetriese hoeveelheid water, vaste stowwe, en maalmedia in die meul. Vaste stowwe verwys na alle erts wat klein genoeg is om deur die uitskeidingsif aan die ontslagpunt van die meul te vloei. Maalmedia verwys na rotse en staalballe in die meul, met rotse wat te groot is om deur die uitskeidingsif te vloei. Die waarnemingsmodel maak gebruik van die ontslaantempo en die opeenhopingstempo van vaste stowwe as parameters. Indien die meul se ontslagvloeitempo, ontslagdigtheid, en totale volumetriese aanhouding gemeet word, is alle toestande en parameters van die waarnemingsmodel lineêr waarneembaar. Alhoewel instrumentasie by die meul se ontslagpunt as gevolg van ruimte beperkings nog nie op industriële aanlegte ingesluit word nie, dui hierdie studie die voordele aan wat verkrygbaar is deur sulke instrumentasie in te sluit. 'n Verlengde Kalman Filter (VKF) word in simulasie gebruik om die model se toestande en parameters af te skat. 'n Bestaande maalmeul simulasie model vanuit die literatuur word gebruik om die nodige data vir die VKF te genereer. Resultate dui aan dat indien die metings akkuraat genoeg is, veral by die ontslagpunt van die meul, betroubare afskattings van die volumetriese hoeveelheid maalmedia, vaste stowwe, en water in die meul gemaak kan word. So 'n afskatter kan vorentoe gebruik word as deel van 'n gevorderde prosesbeheer strategie.
Thesis (PhD)--University of Pretoria, 2016.
Electrical, Electronic and Computer Engineering
PhD
Unrestricted

An embedded model predictive controller for velocity control of trucks is developed and tested. By using a simple model of a heavy duty vehicle and knowledge about the slope of the road ahead, the fuel consumption while traveling near a set speed is diminished by almost 1% on an example road compared to a rule based speed control system. The problem is formulated as a look-ahead optimization problem were fuel consumption and total trip time have to be minimized. To find the optimal solution dynamic programming is used, and the whole code is designed to run on a Scania gearbox ECU in parallel with all the current software. Simulations were executed in a Simulink environment, and two test rides were performed on the E4 motorway.
En algoritm för hastighetsstyrning baserad på modell-prediktiv reglering har utvecklats och testats på befintlig styrsystem i ett Scania lastbil. Genom att använda en enkel modell av fordonet och kunskap om lutningen på vägen framför den kunde man sänka bränsleförbrukningen med nästan 1% i vissa sträckor, jämfört med en regelbaserad farthållare. Problemet är formulerat som en optimerings-problem där bränsleförbrukning och total restid måste minimeras. För att hitta den optimala lösningen användes dynamisk programmering och hela koden är skriven så att den kan exekveras på en Scania styrenehet. Koden är kan köras parallellt med den mjukvara som är installerad på styrenheten. Simuleringar utfördes i en miljö utvecklad i Simulink. Två test-körningar på E4 motorvägen utfördes.

Battery energy management plays a crucial role in fuel economy improvement of charge-sustaining parallel hybrid electric vehicles. Currently available control strategies consider battery state of charge (SOC) and driver’s request through the pedal input in decision-making. This method does not achieve an optimal performance for saving fuel or maintaining appropriate SOC level, especially during the operation in extreme driving conditions or hilly terrain. The objective of this thesis is to develop a control algorithm using forthcoming traffic condition and road elevation, which could be fed from navigation systems. This would enable the controller to predict potential of regenerative charging to capture cost-free energy and intentionally depleting battery energy to assist an engine at high power demand. The starting point for this research is the modelling of a small sport-utility vehicle by the analysis of the vehicles currently available in the market. The result of the analysis is used in order to establish a generic mild hybrid powertrain model, which is subsequently examined to compare the performance of controllers. A baseline is established with a conventional powertrain equipped with a spark ignition direct injection engine and a continuously variable transmission. Hybridisation of this vehicle with an integrated starter alternator and a traditional rule-based control strategy is presented. Parameter optimisation in four standard driving cycles is explained, followed by a detailed energy flow analysis. An additional potential improvement is presented by dynamic programming (DP), which shows a benefit of a predictive control. Based on these results, a predictive control algorithm using fuzzy logic is introduced. The main tools of the controller design are the DP, adaptive-network-based fuzzy inference system with subtractive clustering and design of experiment. Using a quasi-static backward simulation model, the performance of the controller is compared with the result from the instantaneous control and the DP. The focus is fuel saving and SOC control at the end of journeys, especially in aggressive driving conditions and a hilly road. The controller shows a good potential to improve fuel economy and tight SOC control in long journey and hilly terrain. Fuel economy improvement and SOC correction are close to the optimal solution by the DP, especially in long trips on steep road where there is a large gap between the baseline controller and the DP. However, there is little benefit in short trips and flat road. It is caused by the low improvement margin of the mild hybrid powertrain and the limited future journey information. To provide a further step to implementation, a software-in-the-loop simulation model is developed. A fully dynamic model of the powertrain and the control algorithm are implemented in AMESim-Simulink co-simulation environment. This shows small deterioration of the control performance by driver’s pedal action, powertrain dynamics and limited computational precision on the controller performance.

This thesis develops approximate dynamic programming (ADP) strategies suitable for process control problems aimed at overcoming the limitations of MPC, which are the potentially exorbitant on-line computational requirement and the inability to consider the future interplay between uncertainty and estimation in the optimal control calculation. The suggested approach solves the DP only for the state points visited by closed-loop simulations with judiciously chosen control policies. The approach helps us combat a well-known problem of the traditional DP called 'curse-of-dimensionality,' while it allows the user to derive an improved control policy from the initial ones. The critical issue of the suggested method is a proper choice and design of function approximator. A local averager with a penalty term is proposed to guarantee a stably learned control policy as well as acceptable on-line performance. The thesis also demonstrates versatility of the proposed ADP strategy with difficult process control problems. First, a stochastic adaptive control problem is presented. In this application an ADP-based control policy shows an "active" probing property to reduce uncertainties, leading to a better control performance. The second example is a dual-mode controller, which is a supervisory scheme that actively prevents the progression of abnormal situations under a local controller at their onset. Finally, two ADP strategies for controlling nonlinear processes based on input-output data are suggested. They are model-based and model-free approaches, and have the advantage of conveniently incorporating the knowledge of identification data distribution into the control calculation with performance improvement.

This dissertation deals with some computational and analytic challenges for dynamic process operations using first-principles models. For processes with significant spatial variations, spatially distributed first-principles models can provide accurate physical descriptions, which are crucial for offline dynamic simulation and optimization. However, the large amount of time required to solve these detailed models limits their use for online applications such as nonlinear model predictive control (NMPC). To cope with the computational challenge, we develop computationally efficient and accurate dynamic reduced order models which are tractable for NMPC using temporal and spatial model reduction techniques. Then we introduce an input and state blocking strategy for NMPC to further enhance computational efficiency. To improve the overall economic performance of process systems, one promising solution is to use economic NMPC which directly optimizes the economic performance based on first-principles dynamic models. However, complex process models bring challenges for the analysis and design of stable economic NMPC controllers. To solve this issue, we develop a simple and less conservative regularization strategy with focuses on a reduced set of states to design stable economic NMPC controllers. In this thesis, we study the operation problems of a solid sorbent-based CO2 capture system with bubbling fluidized bed (BFB) reactors as key components, which are described by a large-scale nonlinear system of partial-differential algebraic equations. By integrating dynamic reduced models and blocking strategy, the computational cost of NMPC can be reduced by an order of magnitude, with almost no compromise in control performance. In addition, a sensitivity based fast NMPC algorithm is utilized to enable the online control of the BFB reactor. For economic NMPC study, compared with full space regularization, the reduced regularization strategy is simpler to implement and lead to less conservative regularization weights. We analyze the stability properties of the reduced regularization strategy and demonstrate its performance in the economic NMPC case study for the CO2 capture system.

The automotive industry is required to deal with increasingly stringent legislationfor greenhouse gases. Hybrid Electric Vehicles, HEV, are gaining acceptance as thefuture path of lower emissions and fuel consumption. The increased complexityof multiple prime movers demand more advanced control systems, where futuredriving conditions also becomes interesting. For a plug-in Hybrid Electric Vehicle,PIHEV, it is important to utilize the comparatively inexpensive electric energybefore the driving cycle is complete, this for minimize the cost of the driving cycle,since the battery in a PIHEV can be charged from the grid. A strategy with lengthinformation of the driving cycle from a global positioning system, GPS, couldreduce the cost of driving. This by starting to blend the electric energy with fuelearlier, a strategy called blended driving accomplish this by distribute the electricenergy, that is charged externally, with fuel over the driving cycle, and also ensurethat the battery’s minimum level reaches before the driving cycle is finished. Astrategy called Charge Depleting Charge Sustaining, CDCS, does not need lengthinformation. This strategy first depletes the battery to a minimum State of Charge,SOC, and after this engages the engine to maintain the SOC at this level. In thisthesis, a variable SOC reference is developed, which is dependent on knowledgeabout the cycle’s length and the current length the vehicle has driven in the cycle.With assistance of a variable SOC reference, is a blended strategy realized. Thisis used to minimize the cost of a driving cycle. A comparison between the blendedstrategy and the CDCS strategy was done, where the CDCS strategy uses a fixedSOC reference. During simulation is the usage of fuel minimized; and the blendedstrategy decreases the cost of the driving missions compared to the CDCS strategy.To solve the energy management problem is a model predictive control used. Thedesigned control system follows the driving cycles, is charge sustaining and solvesthe energy management problem during simulation. The system also handlesmoderate model errors.
Fordonsindustrin måste hantera allt strängare lagkrav mot utsläpp av emissioneroch växthusgaser. Hybridfordon har börjat betraktas som den framtida vägenför att ytterligare minska utsläpp och användning av fossila bränslen. Den ökadekomplexiteten från flera olika motorer kräver mera avancerade styrsystem. Begränsningarfrån motorernas energikällor gör att framtida förhållanden är viktigaatt estimera. För plug-in hybridfordon, PIHEV, är det viktigt att använda denvvijämförelsevis billiga elektriska energin innan fordonet har nått fram till slutdestinationen.Batteriets nuvarande energimängd mäts i dess State of Charge, SOC.Genom att utnyttja information om hur långt det är till slutdestinationen från ettGlobal Positioning System, GPS, blandar styrsystemet den elektriska energin medbränsle från början, detta kallas för blandad körning. En strategi som inte hartillgång till hur långt fordonet ska köras kallas Charge Depleting Charge Sustaining,CDCS. Denna strategi använder först energin från batteriet, för att sedanbörja använda förbränningsmotorn när SOC:s miniminivå har nåtts. Strategin attanvända GPS informationen är jämförd med en strategi som inte har tillgång tillinformation om körcykelns längd. Blandad körning använder en variabel SOC referens,till skillnad från CDCS strategin som använder sig av en konstant referenspå SOC:s miniminivå. Den variabla SOC referensen beror på hur långt fordonethar kört av den totala körsträckan, med hjälp av denna realiseras en blandad körning.Från simuleringarna visade det sig att blandad körning gav minskad kostnadför de simulerade körcyklerna jämfört med en CDCS strategi. En modellbaseradprediktionsreglering används för att lösa energifördelningsproblemet. Styrsystemetföljer körcykler och löser energifördelningsproblemet för de olika drivkällorna undersimuleringarna. Styrsystemet hanterar även måttliga modellfel.

Optimization has enabled automated applications in chemical manufacturing such as advanced control and scheduling. These applications have demonstrated enormous benefit over the last few decades and continue to be researched and refined. However, these applications have been developed separately with uncoordinated objectives. This dissertation investigates the unification of scheduling and control optimization schemes. The current practice is compared to early-concept, light integrations, and deeper integrations. This quantitative comparison of economic impacts encourages further investigation and tighter integration. A novel approach combines scheduling and control into a single application that can be used online. This approach implements the discrete-time paradigm from the scheduling community, which matches the approach of the control community. The application is restricted to quadratic form, and is intended as a replacement for systems with linear control. A novel approach to linear time-scaling is introduced to demonstrate the value of including scaled production rates, even with simplified equation forms. The approach successfully demonstrates significant benefit. Finally, the modeling constraints are lifted from the discrete-time approach. Time dependent constraints and parameters (like time-of-day energy pricing) are introduced, enabled by the discrete-time approach, and demonstrate even greater economic value. The more difficult problem calls for further exploration into the relaxation of integer variables and initialization techniques for faster, more reliable solutions. These applications are also capable of replacing both scheduling and control simultaneously. A generic CSTR application is used throughout as a case study on which the integrated optimization schemes are implemented. CSTRs are a common model for applications in most chemical engineering industries, from food and beverage, to petroleum and pharmaceuticals. In the included case study results, segregated control and scheduling schemes are shown to be 30+% less profitable than fully unified approaches during operational periods around severe disturbances. Further, inclusion of time-dependent parameters and constraints improved the open-loop profitability by an additional 13%.

Esta tesis aborda el estudio de la Planificación financiera a corto plazo y la Gerencia de efectivo, a través del movimiento de dinero en las cuentas bancarias que participan en las decisiones financieras importantes de una empresa. La investigación se realiza en el marco de los modelos de planificación financiera corporativa, cuyo desarrollo se ha producido sobre todo en los últimos sesenta años. En particular, el trabajo se enfoca en los Sistemas de concentración de caja y desembolsos (CCDS), utilizados por las empresas para mejorar la planificación y el control de los activos corrientes y la Gerencia de efectivo. El objetivo de un CCDS es concentrar el efectivo disponible en una cuenta bancaria principal para hacer el mejor uso del dinero en grandes cantidades y, así, apoyar las operaciones de inversión y financiamiento. En consecuencia, la motivación principal de la tesis es lograr una representación exacta de un CCDS que permite su simulación numérica, análisis y evaluación, así como la posibilidad de nuevas investigaciones y el desarrollo de algoritmos para el soporte de decisiones financieras, basados en herramientas de la teoría de control. En este sentido, se presenta un modelo de simulación de un CCDS basado en ecuaciones en diferencias y técnicas de ingeniería de sistemas, incluyendo la existencia de retardos. Se supone la existencia de una cuenta principal operada de forma centralizada. La cual recibe transferencias de dinero desde las cuentas de ingreso de cada agencia de la empresa. También desde la cuenta principal, el dinero se transfiere hacia las cuentas de desembolso de las agencias para cubrir los sobregiros. El CCDS incluye también una cuenta de inversión para aprovechar los excedentes de efectivo y una línea de crédito para cubrir los déficits de caja. Adicionalmente, se deriva un modelo equivalente representado por ecuaciones algebraicas usando la transformada Z, posibilitando el uso de técnicas rigurosas de control en el campo financiero. Bajo un enfoque descentralizado sobre el modelo del CCDS, se desarrolla un modelo de control predictivo (MPC) para una cuenta de ingresos, cuya aplicación se extiende a todas las agencias del sistema. Se utiliza Programación dinámica (DP) para el modelo de predicción que, a su vez, incluye un modelo de pronóstico estándar para la incertidumbre. EL MPC se simplifica procurando aliviar algunos de los problemas conocidos cuando DP se aplica bajo incertidumbre. También, se establece un sistema de bandas para la incertidumbre, limitando la entrada del modelo de DP, junto con un regulador de estabilización en forma de cascada que utiliza una ganancia de realimentación lineal. Esta combinación permite determinar un intervalo para la estabilidad del sistema indistintamente del tamaño del horizonte de predicción. La señal de referencia es una función de diente de sierra, que se adapta convenientemente a la política de inventario aplicada. La tesis muestra, en teoría y por medio de simulaciones, que el controlador propuesto cumple su objetivo. Por otra parte, se realiza una adaptación del MPC de la cuenta de ingresos, agregándole tiempo de retardo al modelo, con el propósito de utilizarlo para el control de las cuentas de desembolso. En consecuencia, se ofrecen dos propuestas de MPC para el problema de la cobertura de sobregiro. Por último, se presenta un caso de estudio utilizando datos hipotéticos para probar el modelo de simulación del CCDS. La ejecución del modelo ha permitido realizar un análisis exhaustivo de los resultados mostrando sus potencialidades y la versatilidad para adaptarse a diferentes escenarios realistas. Esta investigación abre un abanico de posibilidades para futuras investigaciones en las que se combinan las técnicas y teorías de la ingeniería de sistemas y de control, aplicados al ámbito financiero corporativo.
This thesis addresses the study of cash management and short-term financial planning through the movement of money in bank accounts involved in the important financial decisions of a firm. The research is carried within the framework of models for corporate financial planning, whose development has mostly occurred in the last sixty years. Particularly, the work focuses on the Cash Concentration and Disbursements Systems (CCDS), which are used by firms for the purpose of improving the planning and control of current assets and cash management. The aim of a CCDS is to concentrate available cash in a main bank account in order to make best use of money in large amounts to support investment and financing operations. Consequently, the main motivation of the thesis is to achieve an accurate representation of a CCDS, allowing its numerical simulation, analysis and evaluation, as well as the subsequent possibility of exploring new researches and the development of algorithms for the financial decisions support, based on tools of control theory. In this regard, a simulation model of a CCDS seen as an inventory management system is presented, based on difference equations and systems engineering techniques including the existence of delays due to banking procedures. The model assumes the existence of a centrally operated main account. This account receives money transfers from the revenue accounts of each agency. Also from the main account, money is transferred to the agencies' disbursements accounts in order to cover overdrafts. There exist an investment account into which any cash surpluses of the main account are deposited and a credit line in order to avoid the cash deficits. The operating rules for the CCDS are defined, and income and financial costs involved are considered. The model represents the flow of money between the identified elements of the system and the flow of money requirements or transfer orders. An equivalent model represented by algebraic equations through the Z-transform is derived, which allows using rigorous control techniques in the field of finance. Based on a decentralized approach on the model of the CCDS, a Model Predictive Control (MPC) for a revenue account is developed, which is applied to all agencies. Dynamic Programming (DP) is used for the prediction model by including a standard forecasting model for uncertainty. Simplifications of the MPC are included seeking alleviate some of the known problems when DP is applied under uncertainty. Moreover, a band for the uncertainty is established to narrow the input of the DP model, together with a stabilizing regulator in cascade fashion using a linear feedback gain (closed-loop). This combination allows determining a range for the system stability regardless of the size of the prediction horizon. The reference signal used is a sawtooth function, which conveniently adapts to the inventory policy applied. Theoretically, and through simulation, it is shown that the proposed controller meets the control objective. The MPC of the revenue account is adapted by adding delay time in order to be used for disbursement accounts. Accordingly, two proposals of a model predictive control are provided on the overdraft coverage problem. Finally, a case study is presented using hypothetical data in order to test the simulation model of the CCDS. Running the model allows performing a comprehensive analysis of results showing its potentialities and the versatility to suit different realistic scenarios. This research opens up a range of possibilities for further research in which techniques and theories of systems engineering and control are combined, applied to corporate financial field.

Today, decision support systems based on predictive modeling are becoming more common, since organizations often collectmore data than decision makers can handle manually. Predictive models are used to find potentially valuable patterns in the data, or to predict the outcome of some event. There are numerous predictive techniques, ranging from simple techniques such as linear regression,to complex powerful ones like artificial neural networks. Complexmodels usually obtain better predictive performance, but are opaque and thus cannot be used to explain predictions or discovered patterns.The design choice of which predictive technique to use becomes even harder since no technique outperforms all others over a large set of problems. It is even difficult to find the best parameter values for aspecific technique, since these settings also are problem dependent.One way to simplify this vital decision is to combine several models, possibly created with different settings and techniques, into an ensemble. Ensembles are known to be more robust and powerful than individual models, and ensemble diversity can be used to estimate the uncertainty associated with each prediction.In real-world data mining projects, data is often imprecise, contain uncertainties or is missing important values, making it impossible to create models with sufficient performance for fully automated systems.In these cases, predictions need to be manually analyzed and adjusted.Here, opaque models like ensembles have a disadvantage, since theanalysis requires understandable models. To overcome this deficiencyof opaque models, researchers have developed rule extractiontechniques that try to extract comprehensible rules from opaquemodels, while retaining sufficient accuracy.This thesis suggests a straightforward but comprehensive method forpredictive modeling in situations with poor data quality. First,ensembles are used for the actual modeling, since they are powerful,robust and require few design choices. Next, ensemble uncertaintyestimations pinpoint predictions that need special attention from adecision maker. Finally, rule extraction is performed to support theanalysis of uncertain predictions. Using this method, ensembles can beused for predictive modeling, in spite of their opacity and sometimesinsufficient global performance, while the involvement of a decisionmaker is minimized.The main contributions of this thesis are three novel techniques that enhance the performance of the purposed method. The first technique deals with ensemble uncertainty estimation and is based on a successful approach often used in weather forecasting. The other twoare improvements of a rule extraction technique, resulting in increased comprehensibility and more accurate uncertainty estimations.

Sponsorship:

This work was supported by the Information Fusion Research

Program (www.infofusion.se) at the University of Skövde, Sweden, in

partnership with the Swedish Knowledge Foundation under grant

2003/0104.

To reduce fossil fuel consumption and carbon emission in the building sector, renewable and low carbon energy technologies are integrated in building energy systems to supply all or part of the building energy demand. In this research, an optimal supervisory controller is designed to optimize the operational cost and the CO2 emission of the integrated energy systems. For this purpose, the building energy system is defined and its boundary, components (subsystems), inputs and outputs are identified. Then a mathematical model of the components is obtained. For mathematical modelling of the energy system, a unified modelling method is used. With this method, many different building energy systems can be modelled uniformly. Two approaches are used; multi-period optimization and hybrid model predictive control. In both approaches the optimization problem is deterministic, so that at each time step the energy consumption of the building, and the available renewable energy are perfectly predicted for the prediction horizon. The controller is simulated in three different applications. In the first application the controller is used for a system consisting of a micro-combined heat and power system with an auxiliary boiler and a hot water storage tank. In this application the controller reduces the operational cost and CO2 emission by 7.31 percent and 5.19 percent respectively, with respect to the heat led operation. In the second application the controller is used to control a farm electrification system consisting of PV panels, a diesel generator and a battery bank. In this application the operational cost with respect to the common load following strategy is reduced by 3.8 percent. In the third application the controller is used to control a hybrid off-grid power system consisting of PV panels, a battery bank, an electrolyzer, a hydrogen storage tank and a fuel cell. In this application the controller maximizes the total stored energies in the battery bank and the hydrogen storage tank.

This report presents an approach on how to utilize information on future states of traffic lights to reduce the energy consumption and trip time for a Heavy Duty Vehicle. Model Predictive Control is proposed as a solution to handle the optimisation on-line and the concept is tested for various prediction horizons in which information can be received. Further on, it is investigated if the implemented controller is robust enough to execute the same task in a scenario where only the current state is known and future states are predicted. Comparison with a reference vehicle demonstrates improved fuel economy as well as reduced trip time when the information is given. It is shown that the results are improved as the prediction horizon is extended, but converges after 400-500 meters. As the phases of the traffic lights are predicted, fuel economy can be improved, but it comes at a price from being non-robust with drastic braking and increased trip time as predictions might be inaccurate.

Every method of energy generation and transmission affects the environment. Under this principle, conventional generation options based on fossil fuels, such as coal, gasoline, diesel, among others, are progressively causing damage to air, climate, water, land, wildlife, landscape, and raising levels of harmful radiation. Renewable technologies are substantially safe and offer a solution to many environmental and social problems associated with fossil and nuclear fuels. Within the electricity generation from non-clean fuels, the transport sector occupies a high percentage of the total emissions. For this reason, the development from only using combustion engine vehicles to hybrid, electric and fuel cell vehicles has been made. In this work, hybrid electric vehicles with fuel cells as the main generation source are studied. Within this analysis, a type of vehicle is characterized, which is an urban service bus. The operating parameters are based on the analysis of the selected speed profiles. Besides, power profiles are generated for the vehicle. Some profiles are chosen, such as the Buenos Aires driving cycle, and the Manhattan driving cycle, whose characteristics of speed, acceleration, and distance are analyzed. The speed profiles have moments when the bus brakes to stop at the respective stops, and in some cases, during the intermediate journeys. We use the concept of regenerative braking and propose as elements of energy storage and recovery, batteries, and supercapacitors. The combination allows a better use of the total braking energy, due to the high power and energy density of the supercapacitors and the battery respectively. Once the structure and type of vehicle have been defined and its components have been modeled, defining their power and energy capacities, the optimum scenario is sought through dynamic programming. Taking into account different multi-objective, cost functions are proposed, which take into account the hydrogen savings in the fuel cell and the health of the components. Results are presented for both profiles and various cost functions, analyzing system behavior and presenting Pareto diagrams for tuning the weights of the respective functions. Then, the EMPC controller is designed, which in addition to the conventional criteria, takes into account the cost of generating the elements. Several simulations are performed with the proposed models and different efficiency values of the components. The analysis of various cost functions is also performed, and the results are compared with dynamic programming and the behavior of the system in the face of various sizes of prediction horizon is analyzed. Finally, a trajectory planning is made, taking into account the number of bus stops, and taking into account the dynamics of the bus operation. In this sense, we obtain certain maximum and minimum speed paths from the driving profiles, which are made from the maximum and minimum acceleration data of the driving profiles. With this trajectory planner, we propose a robust EMPC control, which ensures that the controller is able to meet these new power requirements. The mathematical study of the new controller is performed to ensure stability and reachability characteristics, and the results are presented in comparison with PD and pure EMPC.
Las opciones de generación convencionales basadas en combustibles fósiles, como el carbón, la gasolina, el diésel, entre otros, están progresivamente causando daños al aire, el clima, el agua, la tierra, la vida silvestre, el paisaje, as í como elevar los niveles de radiación dañina. Las tecnologías renovables son sustancialmente más seguras y ofrecen una solución a muchos problemas ambientales y sociales asociados con los combustibles fósiles y nucleares. Dentro de esta generación eléctrica con combustibles no limpios, el sector del transporte ocupa un porcentaje elevado de emisiones, dentro del total. Por esta razón, se ha dado el paso paulatino de los vehículos de motor de combustión solamente, a los vehículos híbridos, eléctricos y de pilas de combustible. En la presente tesis, se estudian los vehículos eléctricos híbridos con pila de combustible como fuente de generación principal. Dentro de este análisis, se caracteriza un tipo de vehículo a usar, el mismo que es un bus de servicio urbano, para el que se definen los parámetros de funcionamiento, y en base a el análisis de los perfiles de velocidad seleccionados, se generan perfiles de potencia a ser cumplidos por el vehículo. Los perfiles escogidos son el Buenos Aires driving cycle, y el Manhattan driving cycle, cuyas características de velocidad, aceleración y distancia, se analizan posteriormente. Los perfiles de velocidad, poseen instantes en donde el autobús, frena para detenerse en las paradas respectivas, y en algunos casos, durante los trayectos intermedios. En este momento, usamos el concepto de frenado regenerativo, y proponemos como elementos de almacenamiento y recuperación de energía, baterías y supercapacitores. La combinación de ambos, permite un mayor aprovechamiento de la energía total del frenado, debido a la alta densidad de potencia y de energía de los supercapacitores y la batería respectivamente. Una vez definida la estructura, tipo de vehículo, y modelizado sus componentes, definiendo sus capacidades de potencia y energía, se proceden a buscar el escenario óptimo mediante la programación dinámica. Para esto, se proponen distintas funciones de coste, multiobjetivo que toman en cuenta el ahorro de hidrogeno en la pila de combustible y el estado de salud de los componentes. Se presentan resultados para ambos perfiles y varias funciones de coste, analizando el comportamiento del sistema y presentando diagramas de pareto para el tunning de los pesos de las funciones respectivas. Luego, se procede al diseño del controlador EMPC, el mismo que además de los criterios convencionales, toma en cuenta el coste de generación de los elementos. Se realizan varias simulaciones con los modelos propuestos, y distintos valores de eficiencia de los componentes. Se realizan también el análisis de varias funciones de coste, y se comparan los resultados con la programación dinámica. Se analiza también el comportamiento del sistema ante varios tamaños de horizonte de predicción. Finalmente, se hace una planificación de trayectorias, tomando en consideración el número de paradas y la dinámica de funcionamiento. Obtenemos trayectorias de velocidades máximas y mínimas a partir de los perfiles, las mismas que se realizan a partir de los datos de aceleración máxima y mínima. Con este Planificador de trayectorias, proponemos un control EMPC robusto, el mismo asegura que el controlador sea capaz de cumplir con estos nuevos requerimientos de potencia. Se realiza el estudio matemático del nuevo controlador para asegurar las características de estabilidad y alcanzabilidad, y se presentan los resultados en comparación con la DP Ye el EMPC puro.
Cadascun dels mètodes de generació i transmissió d’energia afecta el medi ambient. Tenint en compte aquest principi, les opcions de generació convencionals basades en combustibles fòssils com el carbó, la benzina o el dièsel, entre d’altres, perjudiquen progressivament l’aire, el clima, l’aigua, la terra, la vida silvestre i el paisatge, al mateix temps que eleven els nivells de radiació nociva. Les tecnologies renovables ofereixen una solució a molts problemes de caire ambiental i social associats amb els combustibles fòssils i nuclears. Dins de la generació elèctrica emprant combustibles nets, el sector del transport representa un percentatge elevat de les emissions totals. És per aquest motiu que s’està duent a terme una transició paulatina cap a l’ús de vehicles híbrids, elèctrics i basats en piles de combustible, en detriment dels vehicles basats solament en la combustió. La present tesi estudia els vehicles elèctrics híbrids basats en pila de combustible com a font de generació principal. Dins d’aquesta anàlisi es duu a terme una caracterització del tipus de vehicle a utilitzar, un autobús de servei urbà, per al qual es defineixen els paràmetres de funcionament. En base als perfils de velocitat seleccionats, es generen els perfils de potència que els vehicles han d’obeir. Dits perfils són el Buenos Aires driving cycle i el Manhattann driving cycle, les característiques dels quals en termes de velocitat, acceleració i distancia s’analitzen posteriorment. En concret, els perfils de velocitat contemplen les aturades en les respectives parades, i en alguns casos, en trajectes intermedis. En aquests instants, s’utilitza el concepte de frenada regenerativa, i es proposen elements d’emmagatzematge i recuperació d’energia, com ara bateries i supercondensadors. La seva combinació permet un millor aprofitament de l’energia dissipada en la frenada, gràcies a la seva alta densitat de potència i d’energia dels supercondensadors i les bateries, respectivament. Una vegada s’han definit l’estructura i el tipus de vehicle, i els seus components s’han modelat en base a les capacitats de potència i d’energia, es procedeix a buscar l’escenari òptim mitjançant programació dinàmica. A tal efecte, es proposen diverses funcions de cost multiobjectiu que inclouen l’estalvi d’hidrogen de la pila de combustible i l’estat de salut dels components. Es presenten resultats per a ambdós perfils i per a diverses funcions de cost, analitzant-ne el comportament del sistema i presentant diagrames de Pareto per a ajustar els pesos dels diversos termes de les funcions de cost. A continuació es procedeix a dissenyar un controlador econòmic predictiu (sigles en anglès EMPC), que, a més dels criteris convencionals, considera el cost de generació dels elements. Es realitzen diverses simulacions amb els models proposats, per a diversos valors d’eficiència dels components. A més, també s’analitzen diverses funcions de cost, i es comparen els resultats amb els obtinguts mitjançant programació dinàmica. Per altra banda, es considera també l’efecte de l’horitzó de predicció en el comportament del sistema. Finalment, es realitza una planificació de trajectòries tenint en compte el nombre de parades de l’autobús i la dinàmica de funcionament del mateix. En aquest sentit, s’obtenen certes trajectòries de velocitats màximes i mínimes a partir dels perfils de conducció, i també a partir de dades d’acceleració màxima i mínima dels perfils de conducció. Emprant aquest planificador de trajectòries, es proposa un control EMPC robust, que garanteix que el controlador és capaç d’assolir aquests nous requeriments de potència. Així mateix es realitza l’estudi matemàtic del nou controlador per a garantir-ne l’estabilitat i l’assolibilitat, i es presenten els resultats comparats amb els proporcionats per la programació dinàmica i el EMPC sense robustesa.

A causa delle alte frequenze di campionamento e delle ridotte risorse computazionali, la certificazione di complessità ha un ruolo chiave nella determinazione del successo del Model Predictive Control (MPC) nelle applicazioni embedded. Questa tesi propone un algoritmo di certificazione per metodi active-set duali, che permette di calcolare esattamente il tempo massimo di risoluzione di un problema di Quadratic Programming (QP) parametrico, risultante ad esempio da formulazioni MPC lineari. Dato un problema MPC e una piattaforma di calcolo è quindi possibile certificare se il problema di ottimizzazione sarà sempre risolto nel limite di tempo. La mancanza di una certificazione è anche una minaccia per la validità dei metodi di accelerazione, dato che il miglioramento del tempo massimo di soluzione è molto più importante di quello medio per embedded MPC. Due nuovi metodi sono presentati per i quali il miglioramento nel caso peggiore è certificabile esattamente. Il primo è un MPC semi-esplicito che combina un risolutore online con la legge multiparametrica delle partizioni poliedrali che incidono maggiormente sul caso peggiore. Il secondo consiste in una selezione alternativa dei vincoli violati per metodi active-set duali, la quale diminuisce sia il numero massimo di iterazioni, sia la complessità della singola iterazione. Infine, la tesi propone applicazioni sperimentali di embedded MPC a motori elettrici e convertitori di potenza. Il controllo di coppia di un motore brushless tramite MPC è validato su un’unità di controllo economica, risultando più veloce della corrispondente soluzione multiparametrica. Viene poi presentato un controllo MPC per convertitori DC-DC pre-compensati per aggirare il problema dei controllori primali non modificabili. Inoltre, è affrontato il problema della stima dello stato per diversi convertitori nella stessa unità di alimentazione, sviluppando un osservatore robusto e non lineare unificato per sei diverse tipologie di convertitori.
Due to the fast sampling frequency and the scarce computational resources, the complexity certification of optimization algorithms plays a key role in determining the success of embedded Model Predictive Control (MPC). This thesis proposes a certification algorithm for dual active-set methods, able to compute exactly the worst-case number of iterations and the amount of time needed to solve a parametric Quadratic Programming (QP) problem, like those that arise in linear MPC. Therefore, given an MPC problem and a computational unit, it can be certified if the optimization problem will be always solved in the prescribed amount of time. The lack of a complexity certification is a threat for accelerating methods as well, as speeding up the worst-case time is much more important than improving the average case in embedded MPC. The thesis presents two novel accelerating methodologies, for which the worst-case improvement can be exactly certified. The first is a semi-explicit MPC, combining an online solver with the multiparametric solution of those polyhedral regions that most affect the worst-case time. The second method consists of an alternative selection for violated constraints in dual active-set solvers, which lowers the worst-case number of iterations and the complexity of the single iteration. Finally, embedded MPC for electrical drives and power converters is experimentally investigated. MPC for the torque control of a brushless motor is demonstrated to be feasible on a cheap control board, and even faster than the corresponding multiparametric solution. Embedded MPC for pre-compensated DC-DC converters is developed, in order to overcome the obstacle of a non-modifiable primal controller, very common in power converters. The issue of estimating the state for multiple DC-DC converters on the same power supply is also addressed, by presenting a unified nonlinear robust observer for six different converter topologies.

The use of positioning systems in a vehicle is a research intensive field. In the first part of this thesis an increase in new applications is disclosed through a mapping of patent documents on how positioning systems can support adaptive cruise control, gear changing systems and engine control. Many ideas are presented and explained and the ideas are valued. Furthermore, a new method for selective catalytic reduction (SCR) control using a positioning system is introduced. It is concluded that look-ahead control, where the vehicle position in relation to the upcoming road section is utilized could give better fuel efficiency, lower emissions and less brake, transmission and engine wear.

In the second part of this thesis a real time test platform for predictive speed control algorithms has been developed and tested in a real truck. Previously such algorithms could

only be simulated. In this thesis an algorithm which utilizes model predictive control (MPC) and dynamic programming (DP) been implemented and evaluated. An initial comparative fuel test shows a reduction in fuel consumption when the MPC algorithm is used.

The operation of groups of heavy-duty vehicles at small inter-vehicular distances, known as platoons, lowers the overall aerodynamic drag and, therefore, reduces fuel consumption and greenhouse gas emissions. Experimental tests conducted on a flat road and without traffic have shown that platooning has the potential to reduce the fuel consumption up to 10%. However, platoons are expected to drive on public highways with varying topography and traffic. Due to the large mass and limited engine power of heavy-duty vehicles, road slopes can have a significant impact on feasible and optimal speed profiles. Therefore, maintaining a short inter-vehicular distance without coordination can result in inefficient or even infeasible speed trajectories. Furthermore, external traffic can interfere by affecting fuel-efficiency and threatening the safety of the platooning vehicles. This thesis addresses the problem of safe and fuel-efficient control for heavy-duty vehicle platooning. We propose a hierarchical control architecture that splits this complex control problem into two layers. The layers are responsible for the fuel-optimal control based on look-ahead information on road topography and the real-time vehicle control, respectively. The top layer, denoted the platoon coordinator, relies on a dynamic programming framework that computes the fuel-optimal speed profile for the entire platoon. The bottom layer, denoted the vehicle control layer, uses a distributed model predictive controller to track the optimal speed profile and the desired inter-vehicular spacing policy. Within this layer, constraints on the vehicles' states guarantee the safety of the platoon. The effectiveness of the proposed controller is analyzed by means of simulations of several realistic scenarios. They suggest a possible fuel saving of up to 12% for the follower vehicles compared to the use of existing platoon controllers. Analysis of the simulation results shows how the majority of the fuel saving comes from a reduced usage of vehicles brakes. A second problem addressed in the thesis is model predictive control for obstacle avoidance and lane keeping for a passenger car. We propose a control framework that allows to control the nonlinear vehicle dynamics with linear model predictive control. The controller decouples the longitudinal and lateral vehicle dynamics into two successive stages. First, plausible braking and throttle profiles are generated. Second, for each profile, linear time-varying models of the lateral dynamics are derived and used to formulate a collection of linear model predictive control problems. Their solution provides the optimal control input for the steering and braking actuators. The performance of the proposed controller has been evaluated by means of simulations and real experiments.

QC 20150911

La gestion de la demande en chauffage des bâtiments raccordés à des réseaux de chaleur s'effectue classiquement au moyen d’une courbe de chauffe : lorsque la température extérieure chute, la température de départ de l’eau alimentant le circuit de chauffage interne est relevée. Ce mode de contrôle, appelé régulation par loi d’eau, présente des atouts en termes de simplicité et de robustesse, mais ne tient pas compte de l'inertie thermique du bâtiment et ne permet donc pas une modulation de sa demande. La modulation de la demande en chauffage se définit comme l'action de contrôle consistant à modifier de manière stratégique les conditions de confort thermique dans le cadre d’une optimisation énergétique et/ou économique. Il s’agit d’une brique essentielle du contrôle flexible qui envisage le déplacement des charges et l’effacement des pics pour une meilleure efficacité de production favorisant la pénétration des énergies renouvelables et de récupération.Ces travaux de thèse visent à développer une stratégie de contrôle prédictif et flexible de la demande en chauffage, applicable à grande échelle dans les réseaux de chaleur.Tout d'abord, un simulateur thermique dynamique de bâtiment résidentiel, équipé de radiateurs hydrauliques connectés à une sous-station de réseau de chaleur, est développé. Il permet de définir plusieurs cas d’études de bâtiments représentatifs du parc résidentiel français et constitue l’environnement expérimental virtuel de nos travaux de recherche. Ensuite, une méthodologie permettant d’obtenir un modèle orienté-contrôle et d’ordre réduit de bâtiment avec son système de chauffage est proposée. Elle commence par la définition de la structure du modèle en se basant sur des connaissances physiques, puis consiste en l'identification des paramètres par optimisation méta-heuristique à l'aide des données générées par le simulateur. L'approche d'identification paramétrique évalue la possibilité de réaliser cette tâche en ne s’appuyant que sur des données disponibles au niveau de la sous-station, notamment en s’interdisant d’utiliser des mesures de température intérieure au bâtiment, donnée à caractère personnel présumée indisponible à grande échelle pour des raisons techniques, économiques et juridiques. Enfin, la stratégie de contrôle prédictif est implémentée. Elle permet la planification de la température de départ de l'eau de chauffage en fonction des prévisions météorologiques et des prix de l’énergie. Le contrôleur flexible s’appuie sur un problème d’optimisation linéaire sous contraintes, selon le principe de l’horizon fuyant. Il incorpore les équations linéarisées du modèle d’ordre réduit et calcule le compromis optimal entre coûts énergétiques et inconfort thermique, le degré de flexibilité de la demande en chauffage étant défini par l’intermédiaire de paramètres de réglage dédiés
In District Heating Systems (DHSs), buildings Space-Heating (SH) demand management conventionally relies on a heating curve: when the outdoor temperature drops, the internal SH system supply water temperature is raised. This control mode, referred to as Weather-Compensation Control (WCC), offers widely recognized assets in terms of simplicity and robustness. However, WCC does not account for the building thermal inertia, and consequently, it does not allow modulation of its demand. SH demand modulation is the control action of strategically altering the indoor thermal comfort conditions within an energetic and/or economic optimization framework. It is a key measure in flexible demand control strategies, which seek loads shifting and peaks shaving to allow sustainable commitment of energy resources in favour of renewable power penetration and waste heat recovery.The work presented in this thesis aims at developing a flexible Model Predictive Control (MPC) strategy for SH demand, applicable at large scale in DHSs.Firstly, a thermal dynamic simulator of a residential building with a radiator SH circuit connected to a DHS substation is developed. It allows the definition of multiple case study buildings, well-representative of the french residential stock, and constitutes the virtual experimental environment for our research. Then, a methodology to obtain a control-oriented Reduced-Order Model (ROM) for the building and its SH system is proposed. It starts by defining the ROM structure based on physical knowledge, and proceeds to parameters identification by meta-heuristic optimization using data generated by the simulator. The parametric identification approach evaluates the possibility of carrying out this task by relying solely on data available at the substation level, refraining from using indoor temperature measurements, personal data assumed to be unavailable at large scale for technical, economic and legal reasons. Finally, MPC is implemented to schedule the SH supply water temperature as function of weather forecasts and energy price variations. The flexible controller is designed to solve a constrained linear optimization problem according to the receding horizon principle. It embeds the linearized ROM equations within the problem formulation and makes an optimal trade-off between energy consumption costs and thermal discomfort, the degree of flexibility to modulate SH demand being defined through dedicated tuning parameters

As vehicles become electrified and more intelligent in terms of sensing, actuation and processing; a number of interesting possibilities arise in controlling vehicle dynamics and driving behavior. Over-actuation with inwheel motors, all wheel steering and active camber is one such possibility, and can facilitate control combinations that push boundaries in energy consumption and safety. Optimal control can be used to investigate the best combinations of control inputs to an over-actuated system. In Part 1, a literature study is performed on the state of art in the field of optimal control, highlighting the strengths and weaknesses of different methods and their applicability to a vehicular system. Out of these methods, Dynamic Programming and Model Predictive Control are of particular interest. Prior work in overactuation, as well as control for reducing tire energy dissipation is studied, and utilized to frame the dynamics, constraints and objective of an optimal control problem. In Part 2, an optimal control problem representing the lateral dynamics of an over-actuated vehicle is formulated, and solved for different objectives using Dynamic Programming. Simulations are performed for standard driving maneuvers, performance parameters are defined, and a system design study is conducted. Objectives include minimizing tire cornering resistance (saving energy) and maintaining the reference vehicle trajectory (ensuring safety), and optimal combinations of input steering and camber angles are derived as a performance benchmark. Following this, Model Predictive Control is used to design an online controller that follows the optimal vehicle state, and studies are performed to assess the suitability of MPC to over-actuation. Simulation models are also expanded to include non-linear tires. Finally, vehicle implementation is considered on the KTH Research Concept Vehicle (RCV) and four vehicle-implementable control cases are presented. To conclude, this thesis project uses methods in optimal control to find candidate solutions to improve vehicle performance thanks to over-actuation. Extensive vehicle tests are needed for a clear indication of the energy saving achievable, but simulations show promising performance improvements for vehicles overactuated with all-wheel steering and active camber.

Predictive statistical modeling shows promise in accurately predicting academic performance for students enrolled in online programs. This approach has proven effective in accurately identifying students who are at-risk enabling instructors to provide instructional intervention. While the potential benefits of statistical modeling is significant, implementations have proven to be complex, costly, and difficult to maintain. To address these issues, the purpose of this study is to develop a fully integrated, automated predictive modeling system (PMS) that is flexible, easy to use, and portable to identify students who are potentially at-risk for not succeeding in a course they are currently enrolled in. Dynamic and static variables from a student system (edX) will be analyzed to predict academic performance of an individual student or entire class. The PMS model framework will include development of an open-source Web application, application programming interface (API), and SQL reporting services (SSRS). The model is based on knowledge discovery database (KDD) approach utilizing inductive logic programming language (ILP) to analyze student data. This alternative approach for predicting academic performance has several unique advantages over current predictive modeling techniques in use and is a promising new direction in educational research.

This thesis describes the theory of model predictive control and application of the theory to synchronous drives. It shows explicit and on-line solutions and compares the results with classical vector control structure.

This dissertation focuses on constrained control of two applications: helicopter and ocean current turbines (OCT). A major contribution in the helicopter application is a novel model predictive control (MPC) framework for helicopter shipboard operations in high demanding sea-based conditions. A complex helicopter-ship dynamics interface has been developed as a system of implicit nonlinear ordinary differential equations to capture essential characteristics of the nonlinear helicopter dynamics, the ship dynamics, and the ship airwake interactions. Various airwake models such as Control Equivalent Turbulence Inputs (CETI) model and Computation Fluid Dynamics (CFD) data of the airwake are incorporated in the interface to describe a realistic model of the shipborne helicopter. The feasibility of the MPC design is investigated using two case studies: automatic deck landing during the ship quiescent period in sea state 5, and lateral reposition toward the ship in different wind-over-deck conditions. To improve the overall MPC performance, an updating scheme for the internal model of the MPC is proposed using linearization around operating points. A mixed-integer MPC algorithm is also developed for helicopter precision landing on moving decks. The performance of this control structure is evaluated via numerical simulations of the automatic deck landing in adverse conditions such as landing on up-stroke, and down-stroke moving decks with high energy indices. Kino-dynamic motion planning for coordinated maneuvers to satisfy the helicopter-ship rendezvous conditions is implemented via mixed integer quadratic programming. In the OCT application, the major contribution is that a new idea is leveraged from helicopter blade control by introducing cyclic blade pitch control in OCT. A minimum energy, constrained control method, namely Output Variance Constrained (OVC) control is studied for OCT flight control in the presence of external disturbances. The minimum achievable output variance bounds are also computed and a parametric study of design parameters is conducted to evaluate their influence on the OVC performance. The performance of the OVC control method is evaluated both on the linear and nonlinear OCT models. Furthermore, control design for the OCT with sensor failures is also examined. Lastly, the MPC strategy is also investigated to improve the OCT flight control performance in simultaneous satisfaction of multiple constraints and to avoid blade stall.
Ph. D.

Trucks are responsible for the major part of inland freight and so, they are a backbone of the modern economy but they are also a large consumer of energy. In this context, a dominating vehicle is a truck with heavy load on a long trip. The aim with look-ahead control is to reduce the energy consumption of heavy vehicles by utilizing information about future conditions focusing on the road topography ahead of the vehicle. The possible gains with look-ahead control are evaluated by performing experiments with a truck on highway. A real-time control system based on receding horizon control (RHC) is set up where the optimization problem is solved repeatedly on-line for a certain horizon ahead of the vehicle. The experimental results show that significant reductions of the fuel consumption are achieved, and that the controller structure, where the algorithm calculates set points fed to lower level controllers, has satisfactory robustness to perform well on-board in a real environment. Moreover, the controller behavior has the preferred property of being intuitive, and the behavior is perceived as comfortable and natural by participating drivers and passengers. A well-behaved and efficient algorithm is developed, based on dynamic programing, for the mixed-integer nonlinear minimum-fuel problem. A modeling framework is formulated where special attention is given to properly include gear shifting with physical models. Fuel equivalents are used to reformulate the problem into a tractable form and to construct a residual cost enabling the use of a shorter horizon ahead of the vehicle. Analysis of errors due to discretization of the continuous dynamics and due to interpolation shows that an energy formulation is beneficial for reducing both error sources. The result is an algorithm giving accurate solutions with low computational effort for use in an on-board controller for a fuel-optimal velocity profile and gear selection. The prevailing approach for the look-ahead problem is RHC where main topics are the approximation of the residual cost and the choice of the horizon length. These two topics are given a thorough investigation independent of the method of solving the optimal control problem in each time step. The basis for the fuel equivalents and the residual cost is formed from physical intuition as well as mathematical interpretations in terms of the Lagrange multipliers used in optimization theory. Measures for suboptimality are introduced that enables choosing horizon length with the appropriate compromise between fuel consumption and trip time. Control of a hybrid electric powertrain is put in the framework together with control of velocity and gear. For an efficient solution of the minimum-fuel problem in this case, more fuel equivalence factors and an energy formulation are employed. An application is demonstrated in a design study where it is shown how the optimal trade-off between size and capacity of the electrical system depends on road characteristics, and also that a modestly sized electrical system achieves most of the gain. The contributions develop algorithms, create associated design tools, and carry out experiments. Altogether, a feasible framework is achieved that pave the way for on-board fuel-optimal look-ahead control.

Cette thèse s’intéresse à la programmation certifiée correcte dans le cadre formel fourni par l’assistant de preuve Coq, et conduite par étapes de raffinements, avec l'objectif d’aboutir à un résultat correct par construction. Le langage de programmation considéré est un langage impératif simple, avec affectations, alternatives, séquences, et boucles. La sémantique associée à ce langage est une sémantique relationnelle exprimée dans un cadre prédicatif plus adapté à un plongement dans la théorie des types, plutôt que dans le calcul des relations. Nous étudions la relation entre d’une part la sémantique prédicative et relationnelle que nous avons choisie, et d’autre part une approche plus classique dans le style de la logique de Hoare. En particulier, nous montrons que les deux approches ont en théorie la même puissance. La démarche que nous étudions consiste à certifier, avec l’aide d’un assistant de preuve, les raffinements successifs permettant de passer de la spécification au programme. Nous nous intéressons donc aussi aux techniques de preuve permettant en pratique d’établir la validité des raffinements. Plus précisément, nous utilisons un calcul de la plus faible pré-spécification jouant ici le rôle du calcul de la plus faible pré-condition dans les approches classiques. Afin que l’articulation des étapes de raffinement reste aussi proche que possible de l’activité de programmation, nous formalisons un langage de développement qui permet de décrire l’arborescence des étapes de raffinement, ainsi qu’une logique permettant de raisonner sur ces développements, et de garantir leur correction
This thesis investigates certified programming by stepwise refinement in the framework of the Coq proof assistant. This allows the construction of programs that are correct by construction. The programming language that is considered is a simple imperative language with assignment, selection, sequence, and iteration. The semantics of this language is formalized in a relational and predicative setting, and is shown to be equivalent to an axiomatic semantics in the style of a Hoare logic. The stepwise refinement approach to programming requires that refinement steps from the specification to the program be proved correct. For so doing, we use a calculus of weakest pre-specifications which is a generalisation of the calculus of weakest pre-conditions. Finally, to capture the whole refinement history of a program development, we formalize a design language and a logic for reasoning about program designs in order to establish that all refinement steps are indeed correct. The approach developed during this thesis is entirely mecanised using the Coq proof assistant

Driver behaviour, route choice, road geometry and vehicle characteristics all influence vehicle consumption, gas emission and safety. This thesis designed an optimum driving model that considers the simultaneous needs of an environmentally friendly and safe (eco-safe) driving behaviour. This research was grounded on optimisation techniques in control theory as well as graph theory to obtain the optimal route and speed profile to assist drivers in eco-safe driving. The joint consideration of optimal benefits in terms of road safety and energy consumption was the key innovation of this dissertation.

Thesis (MScEng (Process Engineering))--University of Stellenbosch, 2011.
ENGLISH ABSTRACT: A mineral concentrate drying process consisting of a hot gas generator, a flash dryer and a feeding section is found to be the bottleneck in the platinum concentrate smelting process. This operation is used as a case study for system identification and model-based control of dryers. Based on the availability of a month's worth of dryer data obtained from a historian, a third party modelling and control software vendor is interested in the use of this data for data driven model construction and options for dryer control. The aimed contribution of this research is to use only data driven techniques and attempt an SID experiment and use of this model in a controller found in literature to be applicable to the dryer process. No first principle model was available for simulation or interpretation of results. Data were obtained for the operation from the plant historian, reduced, cleaned and investigated for deterministic information through surrogate data comparison – resulting in usable timeseries from the plant data. The best datasets were used for modelling of the flash dryer and hot gas generator operations individually, with the hot gas generator providing usable results. The dynamic, nonlinear autoregressive models with exogenous inputs were identified by means of a genetic programming with orthogonal least squares toolbox. The timeseries were reconstructed as a latent variable set, or “pseudo-embedding”, using the delay parameters as identified by average mutual information, autocorrelation and false nearest neighbours. The latent variable reconstruction resulted in a large solution space, which need to be investigated for an unknown model structure. Genetic Programming is capable of identifying unknown structures. Freerun prediction stability and sensitivity analysis were used to assess the identified best models for use in model based control. The best two models for the hot gas generator were used in a basic model predictive controller in an attempt to only track set point changes. One step ahead modelling of the flash dryer outlet air temperature was unsuccessful with the best model obtaining a validation R2 = 43%. The lack of process information contained in the available process variables are to blame for the poor model identification. One-step ahead prediction of the hot gas generator resulted in a top model with validation R2 = 77.1%. The best two hot gas generator models were implemented in a model predictive controller constructed in a real time plant data flow simulation. This controller's performance was measured against set point tracking ability. The MPC implementation was unsuccessful due to the poor freerun prediction ability of the models. The controller was found to be unable to optimise the control moves using the model. This is assigned to poor model freerun prediction ability in one of the models and a too complex freerun model structure required. It is expected that the number of degrees of freedom in the freerun model is too much for the optimiser to handle. A successful real time simulation architecture for the plant dataflow could however be constructed in the supplied software. It is recommended that further process measurements, specifically feed moisture content, feed temperature and air humidity, be included for the flash dryer; closed loop system identification be investigated for the hot gas generator; and a simpler model structure with smaller reconstructed latent variable regressor set be used for the model predictive controller.
AFRIKAANSE OPSOMMING: 'n Drogings proses vir mineraal konsentraat bestaan uit drie eenhede: 'n lug verwarmer-, 'n blitsdroeër- en konsentraat toevoer eenheid. Hierdie droeër is geïdentifiseer as die bottelnek in die platinum konsentraat smeltingsproses. Die droeër word gebruik as 'n gevallestudie vir sisteem identifikasie asook model-gebasseerder beheer van droeërs. 'n Maand se data verkry vanaf die proses databasis, het gelei tot 'n derde party industriële sagteware en beheerstelsel maatskappy se belangstelling in data gedrewe modelering en beheer opsies vir die drogings proses. Die doelwit van hierdie studie is om data gedrewe modeleringstegnieke te gebruik en die model in 'n droeër-literatuur relevante beheerder te gebruik. Geen eerste beginsel model is beskikbaar vir simulasie of interpretasie van resultate nie. Die verkrygde data is gereduseer, skoon gemaak en bestudeer om te identifiseer of die tydreeks deterministiese inligting bevat. Dit is gedoen deur die tydreeks met stochastiese surrogaat data te vergelyk. Die mees gepaste datastelle is gebruik vir modellering van die blitsdroeër en lugverwarmer afsonderlik. Die nie-liniêre, dinamiese nie-linieêre outeregressie modelle met eksogene insette was deur 'n genetiese programmering algoritme, met ortogonale minimum kwadrate, identifiseer. Die betrokke tydreeks is omskep in 'n hulp-veranderlike stel deur gebruik te maak van vertragings-parameters wat deur gemiddelde gemeenskaplike inligting, outokorrelasie en vals naaste buurman metodes verkry is. Die GP algoritme is daartoe in staat om the groot oplossings ruimte wat deur hierdie hulp-veranderlike rekonstruksie geskep word, te bestudeer vir 'n onbekende model struktuur. Die vrye vooruitskattings vermoë, asook die model sensitiwiteit is inag geneem tydens die analiese van die resultate. Die beste modelle se gepastheid tot model voorspellende beheer is gemeet deur die uitkomste van 'n sensitiwiteits analise, asook 'n vrylopende voorspelling, in oënskou te neem. Die een-stap vooruit voorspellende model van die droeër was onsusksesvol met die beste model wat slegs 'n validasie R2 = 43% kon behaal. Die gebrekkige meet instrumente in die droeër is te blameer vir die swak resultate. Die een-stap vooruit voorspellende model van die lug verwarmer wat die beste gevaar het, het 'n validasie R2 = 77.1% gehad. 'n Basiese model voorspellende beheerder is gebou deur die 2 beste modelle van slegs die lugverwarmer te gebruik in 'n intydse simulasie van die raffinadery data vloei struktuur. Hierdie beheerder se vermoë om toepaslike beheer uit te oefen, is gemeet deur die slegs die stelpunt te verander. Die beheerder was egter nie daartoe in staat om die insette te optimeer, en so die stelpunt te volg nie. Hierdie onvermoë is as gevolg van die kompleks vrylopende model struktuur wat oor die voorspellingsvenster optimeer moet word, asook die onstabiele vryvooruitspellings vermoë van die modelle. Die vermoede is dat die loslopende voorspelling te veel vryheids grade het om die insette maklik genoeg te optimeer. Die intydse simulasie van die raffinadery se datavloei struktuur was egter suksesvol. Beter meting van noodsaaklike veranderlikes vir die droër, o.a. voginhoud van die voer, voer temperatuur, asook lug humiditeit; geslotelus sisteem identifikasie vir die lugverwarmer; asook meer eenvoudige model struktuur vir gebruik in voorspellende beheer moontlik vermag deur 'n kleiner hulp veranderlike rekonstruksie te gebruik.

O problema da predição da estrutura de proteínas (PPEP) é bastante conhecido na bioinformática. A identificação da conformação nativa de uma proteína permite predizer a sua função no organismo. Este conhecimento também é útil no desenvolvimento de novos fármacos ou na compreensão do mecanismo de várias doenças. Várias técnicas tem sido propostas para resolver este problema. Porém, o alto custo envolvido levou ao surgimento de vários modelos que simplificam, em parte, as estruturas protéicas. No entanto, mesmo com os modelos mais simplificados, a complexidade do problema traz inúmeros desafios computacionais na busca da sua conformação nativa. Este trabalho utiliza o algoritmo evolucionário denominado Evolução Diferenciada (ED) para solucionar o PPEP, representando as proteínas com o modelo AB (toy model), em duas e três dimensões (2D e 3D). O trabalho apresenta a implementação de duas versões da ED, paralelizadas num ambiente de processo em cluster, com Message Passing Interface e arquitetura mestre-escravo. Para a configuração dos operadores do algoritmo de ED, foram realizados vários estudos com diferentes configurações para ambos os modelos, e análises estatísticas determinaram quais os melhores valores. Além disso, foram criados dois operadores especiais: dizimação e mutação espelhada. O primeiro poder ser considerado um operador genérico, que pode ser utilizado em qualquer problema; o segundo é específico para o problema em questão. Além do algoritmo de ED básico, também foi proposta uma versão auto-adaptável, em que alguns de seus parâmetros são atualizados no decorrer da evolução. Os experimentos realizados utilizaram 4 sequências de aminoácidos de benchmark geradas a partir da sequência de Fibonacci, contendo entre 13 e 55 aminoácidos. Os resultados dos algoritmos de ED paralelos foram comparados com os resultados obtidos em outros trabalhos. O algoritmo de ED é capaz de obter resultados excelentes, competitivos com os métodos especializados, apesar de não atingir o ótimo conhecido em algumas instâncias. Os resultados promissores obtidos nesse trabalho mostram que o algoritmo de ED é adequado para o problema. Em trabalhos futuros poderão ser estudados novos operadores especiais ou outras técnicas de inspiração biológica, buscando melhorar os resultados.
Protein structure prediction is a well-known problem in bioinformactis. Identifying protein native conformation makes it possible to predict its function within the organism. Knowing this also helps in the development of new medicines and in comprehending how some illnesses work and act. During the past year some techniques have been proposed to solve this problem, but its high cost made it necessary to build models that simplify the protein structures. However, even with the simplicity of these models identifying the protein native conformation remains a highly complex, computationally challenging problem. This paper uses an evolutionary algorithm known as Differential Evolution (DE) to solve the protein structure prediction problem. The model used to represent the protein structure is the Toy Model (also known as the AB Model) in both 2D and 3D. This work implements two versions of the ED algorithm using a parallel architecture (master-slave) based on Message Passing interface in a cluster. A large number of tests were executed to define the final configuration of the DE operators for both models. A new set of special operators were developed: explosion and mirror mutation. We can consider the first as generic, because it can be used in any problem. The second one is more specific because it requires previous knowledge of the problem. Of the two DE algorithm implemented, one is a basic DE algorithm and the second is a self-adaptive DE. All tests executed in this work used four benchmark amino acid sequences generated from the Fibonacci sequence. Each sequence has 13 to 55 amino acids. The results for both parallel DE algorithms using both 2D and 3D models were compared with other works. The DE algorithm achieved excellent results. It did not achieve the optimal known values for some sequences, but it was competitive with other specialized methods. Overall results encourage further research toward the use of knowledge-based operators and biologically inspired techniques to improve DE algorithm performance.

Nous observons ces dernières années un besoin grandissant dans l’industrie pour des robots capables d’interagir et de coopérer dans des environnements confinés. Cependant, aujourd’hui encore, la définition de trajectoires sûres pour les robots industriels doit être faite manuellement par l’utilisateur et le logiciel ne dispose que de peu d’autonomie pour réagir aux modifications de l’environnement. Cette thèse vise à produire une structure logicielle innovante pour gérer l’évitement d’obstacles en temps réel pour des robots manipulateurs évoluant dans des environnements dynamiques. Nous avons développé pour cela un algorithme temps réel de génération de trajectoires qui supprime de façon automatique l’étape fastidieuse de définition d’une trajectoire sûre pour le robot.La valeur ajoutée de cette thèse réside dans le fait que nous intégrons le problème de contrôle optimal dans le concept de hiérarchie de tâches pour résoudre un problème d’optimisation non-linéaire efficacement et en temps réel sur un système embarqué aux ressources limitées. Notre approche utilise une commande prédictive (MPC) qui non seulement améliore la réactivité de notre système mais présente aussi l’avantage de pouvoir produire une bonne approximation linéaire des contraintes d’évitement de collision. La stratégie de contrôle présentée dans cette thèse a été validée à l’aide de plusieurs expérimentations en simulations et sur systèmes réels. Les résultats démontrent l’efficacité, la réactivité et la robustesse de cette nouvelle structure de contrôle lorsqu’elle est utilisée dans des environnements dynamiques
In the field of industrial robots, there is a growing need for having cooperative robots that interact with each other and share work spaces. Currently, industrial robotic systems still rely on hard coded motions with limited ability to react autonomously to dynamic changes in the environment. This thesis focuses on providing a novel framework to deal with real-time collision avoidance for robots performing tasks in a dynamic environment. We develop a reactive trajectory generation algorithm that reacts in real time, removes the fastidious optimization process which is traditionally executed by hand by handling it automatically, and provides a practical way of generating locally time optimal solutions.The novelty in this thesis is in the way we integrate the proposed time optimality problem in a task priority framework to solve a nonlinear optimization problem efficiently in real time using an embedded system with limited resources. Our approach is applied in a Model Predictive Control (MPC) setting, which not only improves reactivity of the system but presents a possibility to obtain accurate local linear approximations of the collision avoidance constraint. The control strategies presented in this thesis have been validated through various simulations and real-world robot experiments. The results demonstrate the effectiveness of the new control structure and its reactivity and robustness when working in dynamic environments

Constraint handling is difficult in model predictive control (MPC) of linear differential inclusions (LDIs) and linear parameter varying (LPV) systems. The designer is faced with a choice of using conservative bounds that may give poor performance, or accurate ones that require heavy online computation. This thesis presents a framework to achieve a more flexible trade-off between these two extremes by using a state tube, a sequence of parametrised polyhedra that is guaranteed to contain the future state. To define controllers using a tube, one must ensure that the polyhedra are a sub-set of the region defined by constraints. Necessary and sufficient conditions for these subset relations follow from duality theory, and it is possible to apply these conditions to constrain predicted system states and inputs with only a little conservatism. This leads to a general method of MPC design for uncertain-parameter systems. The resulting controllers have strong theoretical properties, can be implemented using standard algorithms and outperform existing techniques. Crucially, the online optimisation used in the controller is a convex problem with a number of constraints and variables that increases only linearly with the length of the prediction horizon. This holds true for both LDI and LPV systems. For the latter it is possible to optimise over a class of gain-scheduled control policies to improve performance, with a similar linear increase in problem size. The framework extends to stochastic LDIs with chance constraints, for which there are efficient suboptimal methods using online sampling. Sample approximations of chance constraint-admissible sets are generally not positively invariant, which motivates the novel concept of ‘sample-admissible' sets with this property to ensure recursive feasibility when using sampling methods. The thesis concludes by introducing a simple, convex alternative to chance-constrained MPC that applies a robust bound to the time average of constraint violations in closed-loop.

Numerical algorithms for efficiently solving optimal control problems are important for commonly used advanced control strategies, such as model predictive control (MPC), but can also be useful for advanced estimation techniques, such as moving horizon estimation (MHE). In MPC, the control input is computed by solving a constrained finite-time optimal control (CFTOC) problem on-line, and in MHE the estimated states are obtained by solving an optimization problem that often can be formulated as a CFTOC problem. Common types of optimization methods for solving CFTOC problems are interior-point (IP) methods, sequential quadratic programming (SQP) methods and active-set (AS) methods. In these types of methods, the main computational effort is often the computation of the second-order search directions. This boils down to solving a sequence of systems of equations that correspond to unconstrained finite-time optimal control (UFTOC) problems. Hence, high-performing second-order methods for CFTOC problems rely on efficient numerical algorithms for solving UFTOC problems. Developing such algorithms is one of the main focuses in this thesis. When the solution to a CFTOC problem is computed using an AS type method, the aforementioned system of equations is only changed by a low-rank modification between two AS iterations. In this thesis, it is shown how to exploit these structured modifications while still exploiting structure in the UFTOC problem using the Riccati recursion. Furthermore, direct (non-iterative) parallel algorithms for computing the search directions in IP, SQP and AS methods are proposed in the thesis. These algorithms exploit, and retain, the sparse structure of the UFTOC problem such that no dense system of equations needs to be solved serially as in many other algorithms. The proposed algorithms can be applied recursively to obtain logarithmic computational complexity growth in the prediction horizon length. For the case with linear MPC problems, an alternative approach to solving the CFTOC problem on-line is to use multiparametric quadratic programming (mp-QP), where the corresponding CFTOC problem can be solved explicitly off-line. This is referred to as explicit MPC. One of the main limitations with mp-QP is the amount of memory that is required to store the parametric solution. In this thesis, an algorithm for decreasing the required amount of memory is proposed. The aim is to make mp-QP and explicit MPC more useful in practical applications, such as embedded systems with limited memory resources. The proposed algorithm exploits the structure from the QP problem in the parametric solution in order to reduce the memory footprint of general mp-QP solutions, and in particular, of explicit MPC solutions. The algorithm can be used directly in mp-QP solvers, or as a post-processing step to an existing solution.
Numeriska algoritmer för att effektivt lösa optimala styrningsproblem är en viktig komponent i avancerade regler- och estimeringsstrategier som exempelvis modellprediktiv reglering (eng. model predictive control (MPC)) och glidande horisont estimering (eng. moving horizon estimation (MHE)). MPC är en reglerstrategi som kan användas för att styra system med flera styrsignaler och/eller utsignaler samt ta hänsyn till exempelvis begränsningar i styrdon. Den grundläggande principen för MPC och MHE är att styrsignalen och de estimerade variablerna kan beräknas genom att lösa ett optimalt styrningsproblem. Detta optimeringsproblem måste lösas inom en kort tidsram varje gång som en styrsignal ska beräknas eller som variabler ska estimeras, och således är det viktigt att det finns effektiva algoritmer för att lösa denna typ av problem. Två vanliga sådana är inrepunkts-metoder (eng. interior-point (IP)) och aktivmängd-metoder (eng. active-set (AS)), där optimeringsproblemet löses genom att lösa ett antal enklare delproblem. Ett av huvudfokusen i denna avhandling är att beräkna lösningen till dessa delproblem på ett tidseffektivt sätt genom att utnyttja strukturen i delproblemen. Lösningen till ett delproblem beräknas genom att lösa ett linjärt ekvationssystem. Detta ekvationssystem kan man exempelvis lösa med generella metoder eller med så kallade Riccatirekursioner som utnyttjar strukturen i problemet. När man använder en AS-metod för att lösa MPC-problemet så görs endast små strukturerade ändringar av ekvationssystemet mellan varje delproblem, vilket inte har utnyttjats tidigare tillsammans med Riccatirekursionen. I denna avhandling presenteras ett sätt att utnyttja detta genom att bara göra små förändringar av Riccatirekursionen för att minska beräkningstiden för att lösa delproblemet. Idag har behovet av  parallella algoritmer för att lösa MPC och MHE problem ökat. Att algoritmerna är parallella innebär att beräkningar kan ske på olika delar av problemet samtidigt med syftet att minska den totala verkliga beräkningstiden för att lösa optimeringsproblemet. I denna avhandling presenteras parallella algoritmer som kan användas i både IP- och AS-metoder. Algoritmerna beräknar lösningen till delproblemen parallellt med ett förutbestämt antal steg, till skillnad från många andra parallella algoritmer där ett okänt (ofta stort) antal steg krävs. De parallella algoritmerna utnyttjar problemstrukturen för att lösa delproblemen effektivt, och en av dem har utvärderats på parallell hårdvara. Linjära MPC problem kan också lösas genom att utnyttja teori från multiparametrisk kvadratisk programmering (eng. multiparametric quadratic programming (mp-QP)) där den optimala lösningen beräknas i förhand och lagras i en tabell, vilket benämns explicit MPC. I detta fall behöver inte MPC problemet lösas varje gång en styrsignal beräknas, utan istället kan den förberäknade optimala styrsignalen slås upp. En nackdel med mp-QP är att det krävs mycket plats i minnet för att spara lösningen. I denna avhandling presenteras en strukturutnyttjande algoritm som kan minska behovet av minne för att spara lösningen, vilket kan öka det praktiska användningsområdet för mp-QP och explicit MPC.

Distributed parameter systems (DPS) comprise an important class of engineering systems ranging from "traditional" such as tubular reactors, to cutting edge processes such as nano-scale coatings. DPS have been studied extensively and significant advances have been noted, enabling their accurate simulation. To this end a variety of tools have been developed. However, extending these advances for systems design is not a trivial task . Rigorous design and operation policies entail systematic procedures for optimisation and control. These tasks are "upper-level" and utilize existing models and simulators. The higher the accuracy of the underlying models, the more the design procedure benefits. However, employing such models in the context of conventional algorithms may lead to inefficient formulations. The optimisation and control of DPS is a challenging task. These systems are typically discretised over a computational mesh, leading to large-scale problems. Handling the resulting large-scale systems may prove to be an intimidating task and requires special methodologies. Furthermore, it is often the case that the underlying physical phenomena span various temporal and spatial scales, thus complicating the analysis. Stiffness may also potentially be exhibited in the (nonlinear) models of such phenomena. The objective of this work is to design reliable and practical procedures for the optimisation and control of DPS. It has been observed in many systems of engineering interest that although they are described by infinite-dimensional Partial Differential Equations (PDEs) resulting in large discretisation problems, their behaviour has a finite number of significant components , as a result of their dissipative nature. This property has been exploited in various systematic model reduction techniques. Of key importance in this work is the identification of a low-dimensional dominant subspace for the system. This subspace is heuristically found to correspond to part of the eigenspectrum of the system and can therefore be identified efficiently using iterative matrix-free techniques. In this light, only low-dimensional Jacobians and Hessian matrices are involved in the formulation of the proposed algorithms, which are projections of the original matrices onto appropriate low-dimensional subspaces, computed efficiently with directional perturbations.The optimisation algorithm presented employs a 2-step projection scheme, firstly onto the dominant subspace of the system (corresponding to the right-most eigenvalues of the linearised system) and secondly onto the subspace of decision variables. This algorithm is inspired by reduced Hessian Sequential Quadratic Programming methods and therefore locates a local optimum of the nonlinear programming problem given by solving a sequence of reduced quadratic programming (QP) subproblems . This optimisation algorithm is appropriate for systems with a relatively small number of decision variables. Inequality constraints can be accommodated following a penalty-based strategy which aggregates all constraints using an appropriate function , or by employing a partial reduction technique in which only equality constraints are considered for the reduction and the inequalities are linearised and passed on to the QP subproblem . The control algorithm presented is based on the online adaptive construction of low-order linear models used in the context of a linear Model Predictive Control (MPC) algorithm , in which the discrete-time state-space model is recomputed at every sampling time in a receding horizon fashion. Successive linearisation around the current state on the closed-loop trajectory is combined with model reduction, resulting in an efficient procedure for the computation of reduced linearised models, projected onto the dominant subspace of the system. In this case, this subspace corresponds to the eigenvalues of largest magnitude of the discretised dynamical system. Control actions are computed from low-order QP problems solved efficiently online.The optimisation and control algorithms presented may employ input/output simulators (such as commercial packages) extending their use to upper-level tasks. They are also suitable for systems governed by microscopic rules, the equations of which do not exist in closed form. Illustrative case studies are presented, based on tubular reactor models, which exhibit rich parametric behaviour.

Genetic programming is an Evolutionary Computing technique, inspired by biological evolution, capable of discovering complex non-linear patterns in large datasets. Genetic programming is a general methodology, the specific implementation of which requires development of several different specific elements such as problem representation, fitness, selection and genetic variation. Despite the potential advantages of genetic programming over standard statistical methods, its applications to survival analysis are at best rare, primarily because of the difficulty in handling censored data. The aim of this work was to develop a genetic programming approach for survival analysis and demonstrate its utility for the automatic development of clinical prediction models using cardiovascular disease as a case study. We developed a tree-based untyped steady-state genetic programming approach for censored longitudinal data, comparing its performance to the de facto statistical method—Cox regression—in the development of clinical prediction models for the prediction of future cardiovascular events in patients with symptomatic and asymptomatic cardiovascular disease, using large observational datasets. We also used genetic programming to examine the prognostic significance of different risk factors together with their non-linear combinations for the prognosis of health outcomes in cardiovascular disease. These experiments showed that Cox regression and the developed steady-state genetic programming approach produced similar results when evaluated in common validation datasets. Despite slight relative differences, both approaches demonstrated an acceptable level of discriminative and calibration at a range of times points. Whilst the application of genetic programming did not provide more accurate representations of factors that predict the risk of both symptomatic and asymptomatic cardiovascular disease when compared with existing methods, genetic programming did offer comparable performance. Despite generally comparable performance, albeit in slight favour of the Cox model, the predictors selected for representing their relationships with the outcome were quite different and, on average, the models developed using genetic programming used considerably fewer predictors. The results of the genetic programming confirm the prognostic significance of a small number of the most highly associated predictors in the Cox modelling; age, previous atherosclerosis, and albumin for secondary prevention; age, recorded diagnosis of ’other’ cardiovascular disease, and ethnicity for primary prevention in patients with type 2 diabetes. When considered as a whole, genetic programming did not produce better performing clinical prediction models, rather it utilised fewer predictors, most of which were the predictors that Cox regression estimated be most strongly associated with the outcome, whilst achieving comparable performance. This suggests that genetic programming may better represent the potentially non-linear relationship of (a smaller subset of) the strongest predictors. To our knowledge, this work is the first study to develop a genetic programming approach for censored longitudinal data and assess its value for clinical prediction in comparison with the well-known and widely applied Cox regression technique. Using empirical data this work has demonstrated that clinical prediction models developed by steady-state genetic programming have predictive ability comparable to those developed using Cox regression. The genetic programming models were more complex and thus more difficult to validate by domain experts, however these models were developed in an automated fashion, using fewer input variables, without the need for domain specific knowledge and expertise required to appropriately perform survival analysis. This work has demonstrated the strong potential of genetic programming as a methodology for automated development of clinical prediction models for diagnostic and prognostic purposes in the presence of censored data. This work compared untuned genetic programming models that were developed in an automated fashion with highly tuned Cox regression models that was developed in a very involved manner that required a certain amount of clinical and statistical expertise. Whilst the highly tuned Cox regression models performed slightly better in validation data, the performance of the automatically generated genetic programming models were generally comparable. The comparable performance demonstrates the utility of genetic programming for clinical prediction modelling and prognostic research, where the primary goal is accurate prediction. In aetiological research, where the primary goal is to examine the relative strength of association between risk factors and the outcome, then Cox regression and its variants remain as the de facto approach.

This research studies how to efficiently predict optimal active constraints of an inequality constrained optimization problem, in the context of Interior Point Methods (IPMs). We propose a framework based on shifting/perturbing the inequality constraints of the problem. Despite being a class of powerful tools for solving Linear Programming (LP) problems, IPMs are well-known to encounter difficulties with active-set prediction due essentially to their construction. When applied to an inequality constrained optimization problem, IPMs generate iterates that belong to the interior of the set determined by the constraints, thus avoiding/ignoring the combinatorial aspect of the solution. This comes at the cost of difficulty in predicting the optimal active constraints that would enable termination, as well as increasing ill-conditioning of the solution process. We show that, existing techniques for active-set prediction, however, suffer from difficulties in making an accurate prediction at the early stage of the iterative process of IPMs; when these techniques are ready to yield an accurate prediction towards the end of a run, as the iterates approach the solution set, the IPMs have to solve increasingly ill-conditioned and hence difficult, subproblems. To address this challenging question, we propose the use of controlled perturbations. Namely, in the context of LP problems, we consider perturbing the inequality constraints (by a small amount) so as to enlarge the feasible set. We show that if the perturbations are chosen judiciously, the solution of the original problem lies on or close to the central path of the perturbed problem. We solve the resulting perturbed problem(s) using a path-following IPM while predicting on the way the active set of the original LP problem; we find that our approach is able to accurately predict the optimal active set of the original problem before the duality gap for the perturbed problem gets too small. Furthermore, depending on problem conditioning, this prediction can happen sooner than predicting the active set for the perturbed problem or for the original one if no perturbations are used. Proof-of-concept algorithms are presented and encouraging preliminary numerical experience is also reported when comparing activity prediction for the perturbed and unperturbed problem formulations. We also extend the idea of using controlled perturbations to enhance the capabilities of optimal active-set prediction for IPMs for convex Quadratic Programming (QP) problems. QP problems share many properties of LP, and based on these properties, some results require more care; furthermore, encouraging preliminary numerical experience is also presented for the QP case.