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Dissertations / Theses on the topic 'Nonlinear control methods'
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1
Cho, Dong-Il. "Nonlinear control methods for automotive powertrain systems." Thesis, Massachusetts Institute of Technology, 1987. http://hdl.handle.net/1721.1/14682.
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Benouarets, Mourad. "Some design methods for linear and nonlinear controllers." Thesis, University of Sussex, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.333454.
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Huynh, Nguyen. "Digital control and monitoring methods for nonlinear processes." Link to electronic thesis, 2006. http://www.wpi.edu/Pubs/ETD/Available/etd-100906-083012/.
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Dissertation (Ph.D.)--Worcester Polytechnic Institute.<br>Keywords: Parametric optimization; nonlinear dynamics; functional equations; chemical reaction system dynamics; time scale multiplicity; robust control; nonlinear observers; invariant manifold; process monitoring; Lyapunov stability. Includes bibliographical references (leaves 92-98).
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Verschueren, Robin [Verfasser], and Moritz [Akademischer Betreuer] Diehl. "Convex approximation methods for nonlinear model predictive control." Freiburg : Universität, 2018. http://d-nb.info/1192660641/34.
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Blanchard, Eunice Anita. "Exact penalty methods for nonlinear optimal control problems." Thesis, Curtin University, 2014. http://hdl.handle.net/20.500.11937/1805.
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Research comprised of developing solution techniques to three classes of non-standard optimal control problems, namely: optimal control problems with discontinuous objective functions arising in aquaculture operations; impulsive optimal control problems with minimum subsystem durations; optimal control problems involving dual-mode hybrid systems with state-dependent switching conditions. The numerical algorithms developed involved an exact penalty approach to transform the constrained problem into an unconstrained problem which was readily solvable by a standard optimal control software.
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Altafini, Claudio. "Geometric control methods for nonlinear systems and robotic applications." Doctoral thesis, Stockholm : Tekniska högsk, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3151.
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Nanka-Bruce, Oona. "Some computer aided design methods for nonlinear control systems." Thesis, University of Sussex, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.252934.
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Wang, Dazhong. "Polynomial level-set methods for nonlinear dynamics and control /." May be available electronically:, 2007. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.
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Kasnakoglu, Cosku. "Reduced order modeling, nonlinear analysis and control methods for flow control problems." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1195629380.
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Haskara, Ibrahim. "Sliding mode estimation and optimization methods in nonlinear control problems." The Ohio State University, 1999. http://rave.ohiolink.edu/etdc/view?acc_num=osu1250272986.
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Haskara, ?brahim. "Sliding mode estimation and optimization methods in nonlinear control problems /." The Ohio State University, 1999. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488192960166775.
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Rodrigues, Sérgio da Silva. "Methods of nonlinear control theory in problems of mathematical physics." Doctoral thesis, Universidade de Aveiro, 2008. http://hdl.handle.net/10773/2931.
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Doutoramento em Matemática<br>Consideramos a equação de Navier-Stokes num domínio bidimensional e estudamos a sua controlabilidade aproximada e a sua controlabilidade nas projecções em subespaços de campos vectoriais de dimensão finita. Consideramos controlos internos que tomam valores num espaço de dimensão finita. Mais concretamente, procuramos um subespaço de campos vectoriais de divergência nula de dimensão finita de tal modo que seja possível controlar aproximadamente a equação, através de controlos que tomam valores no mesmo subespaço. Usando algumas propriedades de continuidade da equação nos dados iniciais, nomeadamente a continuidade da solução quando o controlo varia na chamada métrica relaxada, reduzimos os resultados em controlabilidade à existência de um chamado conjunto saturante. Consideramos ambas as condições de fronteira do tipo Navier e Dirichlet homogéneas. Damos alguns exemplos de domínios e respectivos conjuntos saturantes. No caso especial das condições de fronteira do tipo Lions - um caso particular das condições do tipo Navier - através de uma técnica envolvendo perturbação analítica de métricas, transferimos a chamada controlabilidade nas projecções em espaços coordenados de dimensão finita de uma métrica para (muitas) outras.<br>We consider the Navier-Stokes equation on a two-dimensional domain and study its approximate controllability and its controllability on projections onto finite-dimensional subspaces of vector fields. We consider body controls taking values in a finite-dimensional space. More precisely we look for a finitedimensional subspace of divergence free vector fields that allow us to control approximately the equation using controls taking values in that subspace. Using some continuity properties of the equation on the initial data, namely the continuity of the solution when the control varies in so-called relaxation metric, we reduce the controllability issues to the existence of a so-called saturating set. Both Navier and no-slip boundary conditions are considered. We present some examples of domains and respective saturating sets. For the special case of Lions boundary conditions - a particular case of Navier boundary conditions - trough a technique involving analytic perturbation of metrics, we transfer so-called controllability on observed coordinate space from one metric to (many) other.
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Haskara, İbrahim. "Sliding mode estimation and optimization methods in nonlinear control problems /." Connect to resource, 1999. http://rave.ohiolink.edu/etdc/view.cgi?acc%5Fnum=osu1250272986.
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McNamara, O. P. "Computer-aided design of nonlinear control systems using describing function based methods." Thesis, University of Sussex, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.375843.
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Dong, Shijie, of Western Sydney Hawkesbury University, and Faculty of Science and Technology. "Robust nonlinear process control by L2 finite gain theory." THESIS_FST_XXX_Dong_S.xml, 1998. http://handle.uws.edu.au:8081/1959.7/386.
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This thesis focuses on nonlinear robust process control synthesis and analysis. The theoretical fundamental is the L2 finite gain theory. The aim of this research is to gain better understanding of this theory and develop new process control synthesis and analysis methods for nonlinear processes with model uncertainties and unmeasured disturbances.The current nonlinear process control methods are examined in this thesis. The research scopes of this study are described as follows: 1/. To characterize the most common process control problems such as zero-offset requirement, presentation of model uncertainties and unknown disturbance in the L2 finite gain theory framework and solve the basic theoretical issues concerned in controller design. 2/. To solve numerical computation problems arising in the nonlinear controller. 3/. To investigate the relationship between robustness requirement and performance requirement for nonlinear systems in the L2 finite gain theory framework. 4/. To consider the common phenomenon such as time-delay in the new developed methods. 5/. To investigate the advantages of the controller based on the L2 finite gain theory over the current nonlinear control methods. A series of new systematic robust process control synthesis approaches are the main contributions of this study. Simulations show the potential of these newly developed methods.<br>Doctor of Philosophy (PhD)
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Tan, Kay Chen. "Evolutionary methods for modelling and control of linear and nonlinear systems." Thesis, University of Glasgow, 1997. http://theses.gla.ac.uk/8473/.
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The aim of this work is to explore the potential and enhance the capability of evolutionary computation for the development of novel and advanced methodologies for engineering system modelling and controller design automation. The key to these modelling and design problems is optimisation. Conventional calculus-based methods currently adopted in engineering optimisation are in essence local search techniques, which require derivative information and lack of robustness in solving practical engineering problems. One objective of this research is thus to develop an effective and reliable evolutionary algorithm for engineering applications. For this, a hybrid evolutionary algorithm is developed, which combines the global search power of a "generational" EA with the interactive local fine-tuning of Boltzmann learning. It overcomes the weakness in local exploration and chromosome stagnation usually encountered in pure EAs. A novel one-integer-one-parameter coding scheme is also developed to significantly reduce the quantisation error, chromosome length and processing overhead time. An "Elitist Direct Inheritance" technique is developed to incorporate with Bolzmann learning for reducing the control parameters and convergence time of EAs. Parallelism of the hybrid EA is also realised in this thesis with nearly linear pipelinability. Generic model reduction and linearisation techniques in L2 and L∞ norms are developed based on the hybrid EA technique. They are applicable to both discrete and continuous-time systems in both the time and the frequency domains. Superior to conventional model reduction methods, the EA based techniques are capable of simultaneously recommending both an optimal order number and optimal parameters by a control gene used as a structural switch. This approach is extended to MIMO system linearisation from both a non-linear model and I/O data of the plant. It also allows linearisation for an entire operating region with the linear approximate-model network technique studied in this thesis. To build an original model, evolutionary black-box and clear-box system identification techniques are developed based on the L2 norm. These techniques can identify both the system parameters and transport delay in the same evolution process. These open-loop identification methods are further extended to closed-loop system identification. For robust control, evolutionary L∞ identification techniques are developed. Since most practical systems are nonlinear in nature and it is difficult to model the dominant dynamics of such a system while retaining neglected dynamics for accuracy, evolutionary grey-box modelling techniques are proposed. These techniques can utilise physical law dominated global clearbox structure, with local black-boxes to include unmeasurable nonlinearities as the coefficient models of the clear-box. This unveils a new way of engineering system modelling. With an accurately identified model, controller design problems still need to be overcome. Design difficulties by conventional analytical and numerical means are discussed and a design automation technique is then developed. This is again enabled by the hybrid evolutionary algorithm in this thesis. More importantly, this technique enables the unification of linear control system designs in both the time and the frequency domains under performance satisfaction. It is also extended to control along a trajectory of operating points for nonlinear systems. In addition, a multi-objective evolutionary algorithm is developed to make the design more transparent and visible. To achieve a step towards autonomy in building control systems, a technique for direct designs from plant step response data is developed, which bypasses the system identification phase. These computer-automated intelligent design methodologies are expected to offer added productivity and quality of control systems.
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Gu, Patrick. "Advanced Nonlinear Control and Estimation Methods for AC Power Generation Systems." Thesis, Southern Illinois University at Edwardsville, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10263630.
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<p> Due to the increased demand for reliable and resilient controls in advanced power generation systems, new control methods are required to tackle traditional problems within these systems. This work discusses a control method and an estimation method for advanced control systems. The control method is sliding mode controls of a higher order, which is used to control the nonlinear wind energy conversion system while lessening the chattering phenomena that causes mechanical wear when using first order sliding mode controls. The super-twisting algorithm is used to create a second order sliding mode control. The estimation method is the derivation of a Resilient Extended Kalman filter, which can estimate and control the system through sensor undergoing failures with a binomial distribution rate and known mean value. Simulations on these dynamical systems are presented to show the effectiveness of the proposed control methods; the former is applied to a wind energy conversion system and the latter is applied to an single machine infinite bus. Both methods are also compared with more traditional methods in their respective applications, those being first order sliding mode controls and the Extended Kalman filter. </p><p>
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Villanueva, Mario Eduardo. "Set-theoretic methods for analysis estimation and control of nonlinear systems." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/32528.
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This thesis is concerned with the application of set-theoretical methods to problems in analysis, estimation and control of nonlinear systems. Set-theoretical concepts are often used in the formulation of various problems in science and engineering. One of the key enablers for the successful application of set-theoretical methods is the ability to enclose the image set of nonlinear multivariate systems, which is the focus of the main body of this thesis. Chapter 2 concentrates on bounding the image of factorable, vector-valued functions. To this aim, a framework is developed which enables the analysis of existing set-valued arithmetics---such as interval and polynomial model arithmetics---and the construction of new ones e.g. an ellipsoidal arithmetic for vector-valued nonlinear factorable functions. This framework also allows to study on a unified way the convergence (in the Hausdorff sense) of the enclosures to the exact image as the domain of the function shrinks. Chapters 3 and 4 are concerned with set propagation through dynamic systems (reachability analysis) defined by parametric ordinary differential equations (ODEs). Computing enclosures for the reachable set is not straightforward, since it is the image of a function which is not factorable, but it is defined implicitly by the ODEs. Nevertheless, computational methods for reachability analysis can take advantage the factorable structure of the ODE right-hand side. The focus on Chapter 3 is on discrete-time set propagation, i.e. methods where the integration horizon is discretized into finite steps, and then propagating the enclosure through each of these steps. Classical methods rely on Taylor expansions of the ODE solution and proceed in two phases. First, an a step-size and an a priori enclosure for the reachable set over the current step are determined. Then, the enclosure is tightened at the end of the step. The algorithm presented in this chapter is also based on Taylor expansions of the solution, but the order of the phases is reversed. This construction leads to a natural step-size control mechanism and eliminates the need for tightening the enclosure at the end of the time-step. Furthermore, sufficient conditions are then derived for the algorithm to be locally asymptotically stable in the neighborhood of a locally asymptotically stable periodic orbit or equilibrium point. The key requirement for stability is that the affine-set extensions used in the propagation have quadratic Hausdorff convergence order. On the other hand, Chapter 4 deals with continuous-time set propagation methods. These class of methods rely on the construction of an auxiliary system of ODEs, whose solution is guaranteed to enclose the reachable set of the original ODEs. Here, a unified framework for the construction of continuous time methods is presented. It is based on a generalized differential inequality (GDI), whose solutions describe the support function of time-varying enclosures for the reachable set. This GDI contains as special cases known continuous-time reachability methods, such as differential inequalities and ellipsoidal set propagation techniques. Although the GDI is based on the support function characterization of convex sets, an extension for nonconvex sets is provided using polynomial models with convex remainders. The framework also provides a means for analyzing the Hausdorff convergence properties of continuous-time enclosure methods. A nontrivial extension of the GDI in the form of a min-max differential inequality is also introduced for the characterization of robust forward invariant tubes. This min-max DI provides as a by product a semi-explicit nonlinear feedback control law, which can also be exploited in robust optimal control and tube-based robust model predictive control. Chapter 5 is concerned with the characterization of sets defined implicitly by systems of constraints. These problems are addressed from a set-theoretical perspective, by adopting the use of complete-search based constraint projection methods. The chapter presents a branch-and-prune algorithm which is enhanced by the use of higher order bounding strategies based on polynomial models. The use of optimization-based domain reduction strategies inspired by developments in branch-and-bound algorithms for complete-search global optimization is also studied. We also introduce a CPU time reduction strategy for polynomial models, which allows reusing the computed bounds whenever they have converged. For constraint systems that include undetermined systems of equations a domain reduction strategy in reduced space is presented. This strategy relies on the use of polynomial models in order to characterize the boundary of the set and makes use of state-of-the-art Newton-like methods for the solution of systems of nonlinear implicit algebraic equations. The algorithm is applied to two different problems: guaranteed parameter estimation and guaranteed asymptotic analysis. The methods in this thesis have been implemented in CRONOS (https://bitbucket.org/omega-icl/cronos), a C++ library that builds upon the MC++ library (https://bitbucket.org/omega-icl/mcpp) for bounding factorable functions. These algorithms have also been tested in a variety of case studies drawn from Chemical Engineering and Systems biology.
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Yan, Fengjun. "Diesel Engine Advanced Multi-Mode Combustion Control and Generalized Nonlinear Transient Trajectory Shaping Control Methods." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1337887426.
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Flayac, Emilien. "Coupled methods of nonlinear estimation and control applicable to terrain-aided navigation." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLY014/document.
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Au cours de cette thèse, le problème général de la conception de méthodes couplées de contrôle et d'estimation pour des systèmes dynamiques non linéaires a été étudié. La cible principale était la navigation par corrélation de terrain (TAN en anglais), où le problème était de guider et d’estimer la position 3D d’un drone survolant une zone connue. Dans cette application, on suppose que les seules données disponibles sont la vitesse du système, une mesure de la différence entre l'altitude absolue du drone et l'altitude du sol survolé et une carte du sol. La TAN est un bon exemple d'application non linéaire dans laquelle le principe de séparation ne peut pas être appliqué. En réalité, la qualité des observations dépend du contrôle et plus précisément de la zone survolée par le drone. Par conséquent, il existe un besoin de méthodes couplées d'estimation et de contrôle. Il est à noter que le problème d'estimation créé par TAN est en soi difficile à analyser et à résoudre. En particulier, les sujets suivants ont été traités:• Conception d'observateur non linéaire et commande en retour de sortie pour la TAN avec des cartes au terrain analytiquesdans un cadre déterministe à temps continu.• La modélisation conjointe du filtrage optimal non linéaire et du contrôle optimal stochastique en temps discretavec des informations imparfaites.• la conception de schémas de contrôle prédictif stochastique duaux associés à un filtre particulaire et leur implémentation numérique pour la TAN<br>During this PhD, the general problem of designing coupled control and estimation methods for nonlinear dynamical systems has been investigated. The main target application was terrain-aided navigation (TAN), where the problem is to guide and estimate the 3D position of a drone flying over a known area. In this application, it is assumed that the only available data are the speed of the system, a measurement of the difference between the absolute altitude of the drone and the altitude of the ground flied over and a map of the ground. TAN is a good example of a nonlinear application where the separation principle cannot be applied. Actually, the quality of the observations depends on the control and more precisely on the area that is flied over by the drone. Therefore, there is a need for coupled estimation and control methods. It is to be noted that the estimation problem created by TAN is in itself difficult to analyse and solve. In particular, the following topics have been treated:• Nonlinear observer design and outputfeedback control for TAN with analytical ground mapsin a deterministic continuous-time framework.• The joint modelling of nonlinear optimal filtering and discrete-time stochastic optimal controlwith imperfect information.• The design of output-feedback Explicit dual stochastic MPC schemes coupled with a particlefilter and their numerical implementation to TAN
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Dong, Shijie. "Robust nonlinear process control by L2 finite gain theory." Thesis, [Richmond, N.S.W.] : Faculty of Science and Technology, University of Western Sydney Hawkesbury, 1998. http://handle.uws.edu.au:8081/1959.7/386.
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This thesis focuses on nonlinear robust process control synthesis and analysis. The theoretical fundamental is the L2 finite gain theory. The aim of this research is to gain better understanding of this theory and develop new process control synthesis and analysis methods for nonlinear processes with model uncertainties and unmeasured disturbances.The current nonlinear process control methods are examined in this thesis. The research scopes of this study are described as follows: 1/. To characterize the most common process control problems such as zero-offset requirement, presentation of model uncertainties and unknown disturbance in the L2 finite gain theory framework and solve the basic theoretical issues concerned in controller design. 2/. To solve numerical computation problems arising in the nonlinear controller. 3/. To investigate the relationship between robustness requirement and performance requirement for nonlinear systems in the L2 finite gain theory framework. 4/. To consider the common phenomenon such as time-delay in the new developed methods. 5/. To investigate the advantages of the controller based on the L2 finite gain theory over the current nonlinear control methods. A series of new systematic robust process control synthesis approaches are the main contributions of this study. Simulations show the potential of these newly developed methods.
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Shoukry, George Fouad. "State-space realization for nonlinear systems." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26497.
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Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2009.<br>Committee Chair: Sadegh, Nader; Committee Member: Chen, Xu-Yan; Committee Member: Chen, Ye-Hwa. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Chen, Liang-kuang. "Describing function methods for the analysis of stability and performance of repetitive control of servohydraulic systems." The Ohio State University, 1996. http://rave.ohiolink.edu/etdc/view?acc_num=osu1102102812.
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Dube, Ntuthuko Marcus. "Development of methods for modelling, parameter and state estimation for nonlinear processes." Thesis, Cape Peninsula University of Technology, 2017. http://hdl.handle.net/20.500.11838/2619.
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Thesis (DTech (Electrical Engineering))--Cape Peninsula University of Technology, 2018.<br>Industrial processes tend to have very complex mathematical models that in
most instances result in very model specific optimal estimation and designs of
control strategies. Such models have many composition components, energy
compartments and energy inventories that result in many process variables that
are intertwined and too complex to separate from one another. Most of the
derived mathematical process models, based on the application of first principles,
are nonlinear and incorporate unknown parameters and unmeasurable states.
This fact results in difficulties in design and implementation of controllers for a
majority of industrial processes. There is a need for the existing parameter and
state estimation methods to be further developed and for new methods to be
developed in order to simplify the process of parameters or states calculation and
be applicable for real-time implementation of various controllers for nonlinear
systems.
The thesis describes the research work done on developing new parameter and
state estimation methods and algorithms for bilinear and nonlinear processes.
Continuous countercurrent ion exchange (CCIX) process for desalination of
water is considered as a case study of a process that can be modelled as a
bilinear system with affine parameters or as purely nonlinear system. Many
models of industrial processes can be presented in such a way. The ion
exchange process model is developed based on the mass balance principle as a
state space bilinear model according to the state and control variables.
The developed model is restructured according to its parameters in order to
formulate two types of parameter estimation problem – with process models
linear and nonlinear according to the parameters. The two models developed are
a bilinear model with affine and a nonlinear according to the parameters model.
Four different methods are proposed for the first case: gradient-based
optimization method that uses the process output measurements, optimization
gradient based method that uses the full state vector measurements, direct
solution using the state vector measurements, and Lagrange’s optimization
technique. Two methods are proposed for the second case: direct solution of the
model equation using MATLAB software and Lagrange’s optimisation
techniques.<br>National Research Foundation (NRF)
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Bürger, Adrian [Verfasser], and Moritz [Akademischer Betreuer] Diehl. "Nonlinear mixed-integer model predictive control of renewable energy systems : : methods, software, and experiments." Freiburg : Universität, 2020. http://d-nb.info/1225682150/34.
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Chai, Qinqin. "Computational methods for solving optimal industrial process control problems." Thesis, Curtin University, 2013. http://hdl.handle.net/20.500.11937/1227.
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In this thesis, we develop new computational methods for three classes of dynamic optimization problems: (i) A parameter identification problem for a general nonlinear time-delay system; (ii) an optimal control problem involving systems with both input and output delays, and subject to continuous inequality state constraints; and (iii) a max-min optimal control problem arising in gradient elution chromatography.In the first problem, we consider a parameter identification problem involving a general nonlinear time-delay system, where the unknown time delays and system parameters are to be identified. This problem is posed as a dynamic optimization problem, where its cost function is to measure the discrepancy between predicted output and observed system output. The aim is to find unknown time-delays and system parameters such that the cost function is minimized. We develop a gradient-based computational method for solving this dynamic optimization problem. We show that the gradients of the cost function with respect to these unknown parameters can be obtained via solving a set of auxiliary time-delay differential systems from t = 0 to t = T. On this basis, the parameter identification problem can be solved as a nonlinear optimization problem and existing optimization techniques can be used. Two numerical examples are solved using the proposed computational method. Simulation results show that the proposed computational method is highly effective. In particular, the convergence is very fast even when the initial guess of the parameter values is far away from the optimal values.Unlike the first problem, in the second problem, we consider a time delay identification problem, where the input function for the nonlinear time-delay system is piecewise-constant. We assume that the time-delays—one involving the state variables and the other involving the input variables—are unknown and need to be estimated using experimental data. We also formulate the problem of estimating the unknown delays as a nonlinear optimization problem in which the cost function measures the least-squares error between predicted output and measured system output. This estimation problem can be viewed as a switched system optimal control problem with time-delays. We show that the gradient of the cost function with respect to the unknown state delay can be obtained via solving a auxiliary time-delay differential system. Furthermore, the gradient of the cost function with respect to the unknown input delay can be obtained via solving an auxiliary time-delay differential system with jump conditions at the delayed control switching time points. On this basis, we develop a heuristic computational algorithm for solving this problem using gradient based optimization algorithms. Time-delays in two industrial processes are estimated using the proposed computational method. Simulation results show that the proposed computational method is highly effective.For the third problem, we consider a general optimal control problem governed by a system with input and output delays, and subject to continuous inequality constraints on the state and control. We focus on developing an effective computational method for solving this constrained time delay optimal control problem. For this, the control parameterization technique is used to approximate the time planning horizon [0, T] into N subintervals. Then, the control is approximated by a piecewise constant function with possible discontinuities at the pre-assigned partition points, which are also called the switching time points. The heights of the piecewise constant function are decision variables which are to be chosen such that a given cost function is minimized. For the continuous inequality constraints on the state, we construct approximating smooth functions in integral form. Then, the summation of these approximating smooth functions in integral form, which is called the constraint violation, is appended to the cost function to form a new augmented cost function. In this way, we obtain a sequence of approximate optimization problems subject to only boundedness constraints on the decision variables. Then, the gradient of the augmented cost function is derived. On this basis, we develop an effective computational method for solving the time-delay optimal control problem with continuous inequality constraints on the state and control via solving a sequence of approximate optimization problems, each of which can be solved as a nonlinear optimization problem by using existing gradient-based optimization techniques. This proposed method is then used to solve a practical optimal control problem arising in the study of a real evaporation process. The results obtained are highly satisfactory, showing that the proposed method is highly effective.The fourth problem that we consider is a max-min optimal control problem arising in the study of gradient elution chromatography, where the manipulative variables in the chromatographic process are to be chosen such that the separation efficiency is maximized. This problem has three non-standard characteristics: (i) The objective function is nonsmooth; (ii) each state variable is defined over a different time horizon; and (iii) the order of the final times for the state variable, the so-called retention times, are not fixed. To solve this problem, we first introduce a set of auxiliary decision variables to govern the ordering of the retention times. The integer constraints on these auxiliary decision variables are approximated by continuous boundedness constraints. Then, we approximate the control by a piecewise constant function, and apply a novel time-scaling transformation to map the retention times and control switching times to fixed points in a new time horizon. The retention times and control switching times become decision variables in the new time horizon. In addition, the max-min objective function is approximated by a minimization problem subject to an additional constraint. On this basis, the optimal control problem is reduced to an approximate nonlinear optimization problem subject to smooth constraints, which is then solved using a recently developed exact penalty function method. Numerical results obtained show that this approach is highly effective.Finally, some concluding remarks and suggestions for further study are made in the conclusion chapter.
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Bergner, Lilli [Verfasser], and Christian [Akademischer Betreuer] Kirches. "Fast numerical methods for robust nonlinear optimal control under uncertainty / Lilli Bergner ; Betreuer: Christian Kirches." Heidelberg : Universitätsbibliothek Heidelberg, 2018. http://d-nb.info/1177385287/34.
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Leidereiter, Conrad [Verfasser], and Hans Georg [Akademischer Betreuer] Bock. "Numerical Methods for Scenario Tree Nonlinear Model Predictive Control / Conrad Leidereiter ; Betreuer: Hans Georg Bock." Heidelberg : Universitätsbibliothek Heidelberg, 2018. http://d-nb.info/1177691760/34.
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Frison, Lilli [Verfasser], and Christian [Akademischer Betreuer] Kirches. "Fast numerical methods for robust nonlinear optimal control under uncertainty / Lilli Bergner ; Betreuer: Christian Kirches." Heidelberg : Universitätsbibliothek Heidelberg, 2018. http://nbn-resolving.de/urn:nbn:de:bsz:16-heidok-242120.
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Martin, Peter. "The development of advanced multivariable, linear and nonlinear control design methods with applications to marine vehicles." Thesis, University of Strathclyde, 2005. http://digitool.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=28873.
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This thesis primarily concerns control and identification of FPSO and Shuttle Tanker vessels, where nonlinear hydrodynamics raise the associated issue of nonlinear control. A 3-DOF model is presented for investigating Dynamic Positioning control, a problem where directional thrusters maintain ship position and heading against environmental disturbances. The coupled, multivariable dynamics are controlled using rapid tuning techniques to decouple the plant, yielding successful multivariable PI feedback designs. Identification of a coupled FPSO and Shuttle Tanker is achieved using an MLP neural network. Initially, the network is trained with simulation data for proof of concept, before employing real data from a Mitsubishi Heavy Industries scale model. Identification is successful, but performance degrades with increasing wave height. Two adaptive controllers are developed, based on polynomial LQG and LQG PC optimal control theory. The first uses a standard stochastic cost, approximated to produce a restricted structure controller that permits optimisation across several plant models at once, yielding a multiple model controller. Augmenting linearised ship models with online identification produces adaptive control giving interesting trade-offs between robustness and performance. The second adaptive controller is very similar, but based on a multi-step predictive cost function. Both controllers are applied to FPSO surge axis velocity control, where the LQGPC version produces better performance for a wave-induced reference. A multivariable nonlinear controller is examined for "sandwich" systems consisting of a linear transfer function "sandwiched" between input and output nonlinearities of a particular form. This system description is substituted into the solution of a time-varying polynomial optimal control problem, where the assumption of a frozen plant at each sampling instant requires slowly-varying plant signals in practice. The controller is successfully applied to a 2 x 2 plant with deadzone input and backlash output, with a demonstration that the performance is superior to a well-tuned linear controller.
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Tarazkar, Maryam. "STRONG FIELD NONLINEAR OPTICS IN ATOMS AND POLYATOMIC MOLECULES: APPLICATION OF QUANTUM MECHANICAL METHODS TO PREDICT AND CONTROL LASER-INDUCED PROCESSES." Diss., Temple University Libraries, 2015. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/364874.
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Chemistry<br>Ph.D.<br>The central objective of this dissertation is developing new methods for calculating higher-order nonlinear optical responses of atoms, molecules, and ions, and discussing the relevant physical mechanisms that give rise to harmonic generation, Kerr effect, and higher-order Kerr effect. The applications of nonlinear optical properties in development of predictive models for femtosecond laser filamentation dynamics, photoemission spectroscopy, imaging, and design of new molecular systems have motivated the theoretical investigations in advancing methods for calculating nonlinear optical properties and finding the optimum conditions for controlling the nonlinearities. The time-dependent nonlinear refractive index coefficient 4 n is investigated for argon and generalized for all noble gas atoms helium, neon, krypton, and xenon in the wavelengths ranging from 250 nm to 2000 nm, using ab initio methods. The secondorder polynomial fitting of DC-Kerr, electric-field-induced second-harmonic generation (ESHG), and static second-order hyperpolarizability have been performed, using an auxiliary electric field approach to obtain the corresponding fourth-order optical properties. An expression on the basis of static, DC-Kerr, DFWM fourth-order hyperpolarizability is derived, which allows the calculations of the DSWM coefficients with considerably reduced error. The results of the calculations suggest that filament stabilization is most likely to be induced by the generation of free electrons. Applications of these calculations resolve the HOKE controversy and are important for the development of predictive models for femtosecond laser filamentation dynamics. In a series of proof-of-concept studies, the approach was employed for calculating dynamic linear and nonlinear hyperpolarizability of the radical cations. In this regard, the polarizability and second-order hyperpolarizability of nitrogen radical cation were investigated, using density functional theory (DFT) and multi-configurational self-consistent field (MCSCF) methods. The open-shell electronic system of nitrogen radical cation provides negative second-order optical nonlinearity, suggesting that the hyperpolarizability coefficient for nitrogen radical cation, in the non-resonant regime is mainly composed of combinations of virtual one-photon transitions rather than two-photon transitions. The calculations of second-order optical properties for nitrogen radical cation as a function of bond length have been investigated to study the effect of internuclear bond distance on optical process. The variation of nonlinear responses versus bond length shows the potential application in finding optimum conditions for higher values of nonlinear coefficients. Furthermore, the computation of dynamic second-order hyperpolarizabilities for multiply ionized noble gases have been studied in the wavelength ranging from 100 nm to the red of the first multi-photon resonance all the way toward the static regime, using the MCSCF method. The results indicate that the second-order hyperpolarizability coefficients decrease when the electrons are removed from the systems. As the atoms reach higher ionization states, the second-order hyperpolarizability responses as a function of wavelength, become less dispersive. The second-order hyperpolarizability coefficients for each ionized species have also been investigated in terms of quantum state symmetries; the results suggest that the sign of the optical responses for each ionized atom depends on the spin of the quantum states defined for the ionized species. The calculations are of value for predictive models of high-harmonic generation in multiply ionized plasma at X-ray photon energies. This research also focuses on investigating possible mechanisms for photodissociation of polyatomic molecules (acetophenone and the substituted derivatives) ionized through strong field infrared laser pulses. In this regard, quantum mechanical methods are combined with pump-probe spectroscopy to understand and control the dissociation dynamics in strong field regime. The applications of quantum mechanical models in interpreting time-resolved wavepacket dynamics and achieving coherent control has stimulated the interest to explore the PESs and investigate the role of conical intersections in wavepacket dynamics in strong field regime. The electronic ground and excited states for acetophenone radical cation and the substituted derivatives have been investigated to probe the resonance features observed in measurements at 1370 nm with laser intensity of 1013 W cm-2. The ten lowest lying ionic potential energy surfaces (PESs) of the acetophenone radical cation were explored, and the three-state conical intersection was mapped onto the PES, using MCSCF model to propose a photo-dissociation mechanism for acetophenone undergoing tunnel ionization and elucidate the potential dissociation pathways for formation of benzoyl fragment ion, as well as phenyl, acylium, and butadienyl small fragment ions. Similar calculations are presented for propiophenone radical cation which support the existence of a one-photon transition from the ground ionic to a bright dissociative D2 state, where motion of the acetyl group from a planar to nonplanar structure within the pulse duration enables the otherwise forbidden transition. The wavepacket dynamics in acetophenone molecular ion is modeled using the classical wavepacket trajectory calculations, to propose the mechanism wherein the 790 nm probe pulse excites a wavepacket on the ground surface D0 to the excited D2 surface at a delay of 325 fs. The innovations of this research are used to design control strategies for selective bond-breaking in acetophenone radical cation, as well as design control schemes for other molecules.<br>Temple University--Theses
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Singla, Puneet. "Multi-resolution methods for high fidelity modeling and control allocation in large-scale dynamical systems." Texas A&M University, 2005. http://hdl.handle.net/1969.1/3785.
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This dissertation introduces novel methods for solving highly challenging model-
ing and control problems, motivated by advanced aerospace systems. Adaptable, ro-
bust and computationally effcient, multi-resolution approximation algorithms based
on Radial Basis Function Network and Global-Local Orthogonal Mapping approaches
are developed to address various problems associated with the design of large scale
dynamical systems. The main feature of the Radial Basis Function Network approach
is the unique direction dependent scaling and rotation of the radial basis function via
a novel Directed Connectivity Graph approach. The learning of shaping and rota-
tion parameters for the Radial Basis Functions led to a broadly useful approximation
approach that leads to global approximations capable of good local approximation
for many moderate dimensioned applications. However, even with these refinements,
many applications with many high frequency local input/output variations and a
high dimensional input space remain a challenge and motivate us to investigate an
entirely new approach. The Global-Local Orthogonal Mapping method is based upon
a novel averaging process that allows construction of a piecewise continuous global
family of local least-squares approximations, while retaining the freedom to vary in
a general way the resolution (e.g., degrees of freedom) of the local approximations.
These approximation methodologies are compatible with a wide variety of disciplines
such as continuous function approximation, dynamic system modeling, nonlinear sig-nal processing and time series prediction. Further, related methods are developed
for the modeling of dynamical systems nominally described by nonlinear differential
equations and to solve for static and dynamic response of Distributed Parameter Sys-
tems in an effcient manner. Finally, a hierarchical control allocation algorithm is
presented to solve the control allocation problem for highly over-actuated systems
that might arise with the development of embedded systems. The control allocation
algorithm makes use of the concept of distribution functions to keep in check the
"curse of dimensionality". The studies in the dissertation focus on demonstrating,
through analysis, simulation, and design, the applicability and feasibility of these ap-
proximation algorithms to a variety of examples. The results from these studies are
of direct utility in addressing the "curse of dimensionality" and frequent redundancy
of neural network approximation.
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Peng, Chen-Chih. "Methods for improving crane performance and ease of use." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/50343.
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Cranes are widely used in material-handling and transportation applications, e.g. in shipyards, construction sites, and warehouses. As they are critical to the economic vitality of modern-day industries, improving crane performance and ease of use are important contributors to industrial productivity, low production costs, and workplace safety.
In a typical crane operation, a payload is lifted, moved to its destination, and then lowered into place. This dissertation aims to improve crane performance and reduce task difficulty for the human operator in the movements mentioned above, namely: 1) Moving payloads laterally in the horizontal plane, 2) Lifting payloads off the ground, and 3) Lowering or laying down payloads on the ground.
The design of a novel and intuitive human-machine control interface is the focus for improving operations that involve moving payloads laterally. The interface allows operators to drive a crane by simply moving a hand-held device through the desired path. The position of the device, which is tracked by sensors, is used to generate command signals to drive the crane. This command is then input-shaped such that payload oscillations are greatly reduced, making it much easier for the operator to drive the crane. Several facets of this crane control method are examined, such as control structure and stability, usability contexts, modes of operation, and quantitative measures (by means of human operator studies) of performance improvements over standard crane control interfaces.
Lifting up a payload can be difficult for the operator, if the hoist is not properly centered above the payload. In these potentially dangerous and costly ``off-centered" lifts, the payload may slide on the ground and/or oscillate in the air after it is hoisted. Newtonian and Coulomb friction models that focus on the stiction-sliding-separation contact dynamics are derived and experimentally verified to study off-centered lifts. Then, with the goal of aiding operators during lift operations, simple but practical, self-centering solutions are proposed and implemented.
Laying down or lowering a payload to the ground can also be challenging for operators in certain situations. For example, laying down a long, slender payload from a vertical orientation in the air, to a horizontal position on a flat surface. If the operator does not properly coordinate the motions of the crane in the vertical and horizontal directions simultaneously, then the potential hazards that may occur during these operations include: 1) slipping of the pivot about which the payload rotates, leading to sudden and dangerous payload movements; and 2) excessive hoist cable angles that lead to ``side-pull" problems. Newtonian and Coulomb friction models are derived to describe this lay-down scenario. The forces and motions experienced by the payload are then used to determine the motion trajectories that the crane and payload should follow to execute a successful lay-down maneuver.
Finally, a special chapter is included to address the oscillation control of systems that have on-off nonlinear actuators, such as cranes powered by relay-controlled circuits. Due to their simplicity, ruggedness, and long service life, this type of crane can be commonly found in older factories or in applications where precise motion control is not a strict requirement. However, controlling payload oscillations on this type of crane is challenging for two reasons: 1) Relays that can only be turned on or off allow for only limited control over the crane velocity; and 2) These cranes typically have nonlinear asymmetrical acceleration and deceleration properties. Methods are derived for determining the relay switch-times that move single-pendulum and double-pendulum payloads with low residual oscillations.
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Wu, Wan. "Analytical and Numerical Methods Applied to Nonlinear Vessel Dynamics and Code Verification for Chaotic Systems." Diss., Virginia Tech, 2009. http://hdl.handle.net/10919/30099.
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In this dissertation, the extended Melnikov's method has been applied to several nonlinear ship dynamics models, which are related to the new generation of stability criteria in the International Maritime Organization (IMO). The advantage of this extended Melnikov's method is it overcomes the limitation of small damping that is intrinsic to the implementation of the standard Melnikov's method.
The extended Melnikv's method is first applied to two published roll motion models. One is a simple roll model with nonlinear damping and cubic restoring moment. The other is a model with a biased restoring moment. Numerical simulations are investigated for both models. The effectiveness and accuracy of the extended Melnikov's method is demonstrated.
Then this method is used to predict more accurately the threshold of global surf-riding for a ship operating in steep following seas. A reference ITTC ship is used here by way of example and the result is compared to that obtained from previously published standard analysis as well as numerical simulations. Because the primary drawback of the extended Melnikov's method is the inability to arrive at a closed form equation, a 'best fit'approximation is given for the extended Melnikov numerically predicted result.
The extended Melnikov's method for slowly varying system is applied to a roll-heave-sway coupled ship model. The Melnikov's functions are calculated based on a fishing boat model. And the results are compared with those from standard Melnikov's method. This work is a preliminary research on the application of Melnikov's method to multi-degree-of-freedom ship dynamics.
In the last part of the dissertation, the method of manufactured solution is applied to systems with chaotic behavior. The purpose is to identify points with potential numerical discrepancies, and to improve computational efficiency. The numerical discrepancies may be due to the selection of error tolerances, precisions, etc. Two classical chaotic models and two ship capsize models are examined. The current approach overlaps entrainment in chaotic control theory. Here entrainment means two dynamical systems have the same period, phase and amplitude. The convergent region from control theory is used to give a rough guideline on identifying numerical discrepancies for the classical chaotic models. The effectiveness of this method in improving computational efficiency is demonstrated for the ship capsize models.<br>Ph. D.
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Qu, Zheng. "Nonlinear Perron-Frobenius theory and max-plus numerical methods for Hamilton-Jacobi equations." Palaiseau, Ecole polytechnique, 2013. http://pastel.archives-ouvertes.fr/docs/00/92/71/22/PDF/thesis.pdf.
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Une approche fondamentale pour la résolution de problémes de contrôle optimal est basée sur le principe de programmation dynamique. Ce principe conduit aux équations d'Hamilton-Jacobi, qui peuvent être résolues numériquement par des méthodes classiques comme la méthode des différences finies, les méthodes semi-lagrangiennes, ou les schémas antidiffusifs. À cause de la discrétisation de l'espace d'état, la dimension des problèmes de contrôle pouvant être abordés par ces méthodes classiques est souvent limitée à 3 ou 4. Ce phénomène est appellé malédiction de la dimension. Cette thèse porte sur les méthodes numériques max-plus en contôle optimal deterministe et ses analyses de convergence. Nous étudions et developpons des méthodes numériques destinées à attenuer la malédiction de la dimension, pour lesquelles nous obtenons des estimations théoriques de complexité. Les preuves reposent sur des résultats de théorie de Perron-Frobenius non linéaire. En particulier, nous étudions les propriétés de contraction des opérateurs monotones et non expansifs, pour différentes métriques de Finsler sur un cône (métrique de Thompson, métrique projective d'Hilbert). Nous donnons par ailleurs une généralisation du "coefficient d'ergodicité de Dobrushin" à des opérateurs de Markov sur un cône général. Nous appliquons ces résultats aux systèmes de consensus ainsi qu'aux équations de Riccati généralisées apparaissant en contrôle stochastique<br>Dynamic programming is one of the main approaches to solve optimal control problems. It reduces the latter problems to Hamilton-Jacobi partial differential equations (PDE). Several techniques have been proposed in the literature to solve these PDE. We mention, for example, finite difference schemes, the so-called discrete dynamic programming method or semi-Lagrangian method, or the antidiffusive schemes. All these methods are grid-based, i. E. , they require a discretization of the state space, and thus suffer from the so-called curse of dimensionality. The present thesis focuses on max-plus numerical solutions and convergence analysis for medium to high dimensional deterministic optimal control problems. We develop here max-plus based numerical algorithms for which we establish theoretical complexity estimates. The proof of these estimates is based on results of nonlinear Perron-Frobenius theory. In particular, we study the contraction properties of monotone or non-expansive nonlinear operators, with respect to several classical metrics on cones (Thompson's metric, Hilbert's projective metric), and obtain nonlinear or non-commutative generalizations of the "ergodicity coefficients" arising in the theory of Markov chains. These results have applications in consensus theory and also to the generalized Riccati equations arising in stochastic optimal control
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Granzotto, Mathieu. "Near-optimal control of discrete-time nonlinear systems with stability guarantees." Electronic Thesis or Diss., Université de Lorraine, 2019. http://www.theses.fr/2019LORR0301.
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L’intelligence artificielle est riche en algorithmes de commande optimale. Il s’agit de générer des entrées de commande pour des systèmes dynamiques afin de minimiser une fonction de coût donnée décrivant l’énergie du système par exemple. Ces méthodes sont applicables à de larges classes de systèmes non-linéaires en temps discret et ont fait leurs preuves dans de nombreuses applications. Leur exploitation en automatique s’avère donc très prometteuse. Une question fondamentale reste néanmoins à élucider pour cela: celle de la stabilité. En effet, ces travaux se concentrent sur l’optimalité et ignorent dans la plupart des cas la stabilité du système commandé, qui est au coeur de l’automatique. L’objectif de ma thèse est d’étudier la stabilité de systèmes non-linéaires commandés par de tels algorithmes. L’enjeu est important car cela permettra de créer un nouveau pont entre l’intelligence artificielle et l’automatique. La stabilité nous informe sur le comportement du système en fonction du temps et garantit sa robustesse en présence de perturbations ou d’incertitudes de modèle. Les algorithmes en intelligence artificielle se concentrent sur l’optimalité de la commande et n’exploitent pas les propriétés de la dynamique du système. La stabilité est non seulement désirable pour les raisons auparavant, mais aussi pour la possibilité de l’exploitée pour améliorer ces algorithmes d’intelligence artificielle. Mes travaux de recherche se concentrent sur les techniques de commande issues de la programmation dynamique (approchée) lorsque le modèle du système est connu. J’identifie pour cela des conditions générales grâce auxquelles il est possible de garantir la stabilité du système en boucle fermée. En contrepartie, une fois la stabilité établie, nous pouvons l’exploiter pour améliorer drastiquement les garanties d’optimalité de la littérature. Mes travaux se sont concentrés autour de deux axes. Le premier concerne l’approche par itération sur les valeurs, qui est l’un des piliers de la programmation dynamique approchée et est au coeur de nombre d’algorithmes d’apprentissage par renforcement. Le deuxième concerne l’approche de planification optimiste, appliqué aux systèmes commutés. J’adapte l’algorithme de planification optimiste pour que, sous hypothèse naturel dans un contexte de stabilisation, obtenir la stabilité en boucle fermé et améliorer drastiquement les garanties d’optimalité de l’algorithme<br>Artificial intelligence is rich in algorithms for optimal control. These generate commands for dynamical systems in order to minimize a a given cost function describing the energy of the system, for example. These methods are applicable to large classes of non-linear systems in discrete time and have proven themselves in many applications. Their application in control problems is therefore very promising. However, a fundamental question remains to be clarified for this purpose: that of stability. Indeed, these studies focus on optimality and ignore in the In most cases the stability of the controlled system, which is at the heart of control theory. The objective of my thesis is to study the stability of non-linear systems controlled by such algorithms. The stakes are high because it will create a new bridge between artificial intelligence and control theory. Stability informs us about the behaviour of the system as a function of time and guarantees its robustness in the presence of model disturbances or uncertainties. Algorithms in artificial intelligence focus on control optimality and do not exploit the properties of the system dynamics. Stability is not only desirable for the reasons mentioned above, but also for the possibility of using it to improve these intelligence algorithms artificial. My research focuses on control techniques from (approximated) dynamic programming when the system model is known. For this purpose, I identify general conditions by which it is possible to guarantee the stability of the closed-loop system. On the other hand, once stability has been established, we can use it to drastically improve the optimality guarantees of literature. My work has focused on two main areas. The first concerns the approach by iteration on values, which is one of the pillars of dynamic programming is approached and is at the heart of many reinforcement learning algorithms. The second concerns the approach by optimistic planning, applied to switched systems. I adapt the optimistic planning algorithm such that, under natural assumptions in an a stabilisation context, we obtain the stability of closed-loop systems where inputs are generated by this modified algorithm, and to drastically improve the optimality guarantees of the generated inputs
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Taylor, Jonathan. "Robust Bode Methods for Feedback Controller Design of Uncertain Systems." Research Showcase @ CMU, 2014. http://repository.cmu.edu/dissertations/447.
Full textAbstract:
In this work, we introduce several novel approaches to feedback controller design, known collectively as the “Robust Bode” methods, which adapt classical control principles to a modern robust control (H∞) framework. These methods, based on specially modified Bode diagrams extend familiar frequency-domain controller design techniques to linear and nonlinear, single–input/single– output (SISO) and multi–input/multi–output (MIMO) systems with parametric and/or unstructured uncertainties. In particular, we introduce the Contoured Robust Controller Bode (CRCBode) plots which show contours (level-sets) of a robust metric on the Bode magnitude and phase plots of the controller. An iterative loop shaping design procedure is then employed in an attempt to eliminate all intersections of the controller frequency response with certain forbidden regions indicating that a robust stability and performance criteria is satisfied. For SISO systems a robust stability and performance criterion is derived using Nyquist arguments leading to the robust metric used in the construction of the CRCBode plots. For open-loop unstable systems and for non-minimum phase systems the Youla parametrization of all internally stabilizing controllers is used to develop an alternative Robust Bode method (QBode). The Youla parametrization requires the introduction of state-space methods for coprime factorization, and these methods lead naturally to an elegant connection between linear-quadratic Gaussian (LQG) optimal control theory and Robust Bode loop-shaping controller design. Finally, the Robust Bode approach is extended to MIMO systems. Utilizing a matrix norm based robustness metric on the MIMO CRCBode plots allows cross-coupling between all input/output channels to be immediately assessed and accounted for during the design process, making sequential MIMO loop-shaping controller design feasible.
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Manuel, Antonio Sánchez Tejada. "Appearance of Symmetry Breaking in AC/AC Converters and Its Recovery Methods." Kyoto University, 2019. http://hdl.handle.net/2433/244550.
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Yerlikaya, Fatma. "A New Contribution To Nonlinear Robust Regression And Classification With Mars And Its Applications To Data Mining For Quality Control In Manufacturing." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/3/12610037/index.pdf.
Full textAbstract:
Multivariate adaptive regression spline (MARS) denotes a modern
methodology from statistical learning which is very important
in both classification and regression, with an increasing number of applications in many areas of science, economy and technology.
MARS is very useful for high dimensional problems and shows a great promise for fitting nonlinear multivariate functions. MARS technique does not impose any particular class of relationship between the predictor variables and outcome variable of interest. In other words, a special advantage of MARS lies in its ability to estimate the contribution of the basis functions so that
both the additive and interaction effects of the predictors are allowed to determine the response variable.
The function fitted by MARS is continuous, whereas the one fitted by classical classification methods (CART) is not. Herewith, MARS becomes an alternative to CART. The MARS algorithm for estimating the model function consists of two complementary algorithms: the forward and backward stepwise algorithms. In the first step, the model is built by adding basis functions until a maximum level of complexity is reached. On the other hand, the backward stepwise algorithm is began by removing the least significant basis functions from the model.
In this study, we propose not to use the backward stepwise algorithm. Instead, we construct a penalized residual sum of squares (PRSS) for MARS as a Tikhonov regularization problem, which is also known as ridge regression. We treat this problem using continuous optimization techniques which we consider to
become an important complementary technology and alternative to the concept of the backward stepwise algorithm. In particular, we apply the elegant framework of conic quadratic programming which is an area of convex optimization that
is very well-structured, herewith, resembling linear programming and, hence, permitting the use of interior point methods. The boundaries of this optimization problem are determined by the multiobjective optimization approach which provides us many
alternative solutions.
Based on these theoretical and algorithmical studies, this MSc thesis work also contains applications on the data investigated in a TÜ<br>BiTAK project on quality control. By these applications, MARS and our new method are compared.
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Halcrow, Jonathan. "Charting the State Space of Plane Couette Flow: Equilibria, Relative Equilibria, and Heteroclinic Connections." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24724.
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Thesis (Ph.D.)--Physics, Georgia Institute of Technology, 2009.<br>Committee Chair: Cvitanovic, Predrag; Committee Member: Bracco, Annalisa; Committee Member: Dieci, Luca; Committee Member: Goldman, Daniel; Committee Member: Grigoriev, Roman
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Reig, Bernad Alberto. "Optimal Control for Automotive Powertrain Applications." Doctoral thesis, Universitat Politècnica de València, 2017. http://hdl.handle.net/10251/90624.
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Optimal Control (OC) is essentially a mathematical extremal problem. The procedure consists on the definition of a criterion to minimize (or maximize), some constraints that must be fulfilled and boundary conditions or disturbances affecting to the system behavior. The OC theory supplies methods to derive a control trajectory that minimizes (or maximizes) that criterion.
This dissertation addresses the application of OC to automotive control problems at the powertrain level, with emphasis on the internal combustion engine. The necessary tools are an optimization method and a mathematical representation of the powertrain. Thus, the OC theory is reviewed with a quantitative analysis of the advantages and drawbacks of the three optimization methods available in literature: dynamic programming, Pontryagin minimum principle and direct methods. Implementation algorithms for these three methods are developed and described in detail. In addition to that, an experimentally validated dynamic powertrain model is developed, comprising longitudinal vehicle dynamics, electrical motor and battery models, and a mean value engine model.
OC can be utilized for three different purposes:
1. Applied control, when all boundaries can be accurately defined. The engine control is addressed with this approach assuming that a the driving cycle is known in advance, translating into a large mathematical problem. Two specific cases are studied: the management of a dual-loop EGR system, and the full control of engine actuators, namely fueling rate, SOI, EGR and VGT settings.
2. Derivation of near-optimal control rules, to be used if some disturbances are unknown. In this context, cycle-specific engine calibrations calculation, and a stochastic feedback control for power-split management in hybrid vehicles are analyzed.
3. Use of OC trajectories as a benchmark or base line to improve the system design and efficiency with an objective criterion. OC is used to optimize the heat release law of a diesel engine and to size a hybrid powertrain with a further cost analysis.
OC strategies have been applied experimentally in the works related to the internal combustion engine, showing significant improvements but non-negligible difficulties, which are analyzed and discussed. The methods developed in this dissertation are general and can be extended to other criteria if appropriate models are available.<br>El Control Óptimo (CO) es esencialmente un problema matemático de búsqueda de extremos, consistente en la definición de un criterio a minimizar (o maximizar), restricciones que deben satisfacerse y condiciones de contorno que afectan al sistema. La teoría de CO ofrece métodos para derivar una trayectoria de control que minimiza (o maximiza) ese criterio.
Esta Tesis trata la aplicación del CO en automoción, y especialmente en el motor de combustión interna. Las herramientas necesarias son un método de optimización y una representación matemática de la planta motriz. Para ello, se realiza un análisis cuantitativo de las ventajas e inconvenientes de los tres métodos de optimización existentes en la literatura: programación dinámica, principio mínimo de Pontryagin y métodos directos. Se desarrollan y describen los algoritmos para implementar estos métodos así como un modelo de planta motriz, validado experimentalmente, que incluye la dinámica longitudinal del vehículo, modelos para el motor eléctrico y las baterías, y un modelo de motor de combustión de valores medios.
El CO puede utilizarse para tres objetivos distintos:
1. Control aplicado, en caso de que las condiciones de contorno estén definidas. Puede aplicarse al control del motor de combustión para un ciclo de conducción dado, traduciéndose en un problema matemático de grandes dimensiones. Se estudian dos casos particulares: la gestión de un sistema de EGR de doble lazo, y el control completo del motor, en particular de las consignas de inyección, SOI, EGR y VGT.
2. Obtención de reglas de control cuasi-óptimas, aplicables en casos en los que no todas las perturbaciones se conocen. A este respecto, se analizan el cálculo de calibraciones de motor específicas para un ciclo, y la gestión energética de un vehículo híbrido mediante un control estocástico en bucle cerrado.
3. Empleo de trayectorias de CO como comparativa o referencia para tareas de diseño y mejora, ofreciendo un criterio objetivo. La ley de combustión así como el dimensionado de una planta motriz híbrida se optimizan mediante el uso de CO.
Las estrategias de CO han sido aplicadas experimentalmente en los trabajos referentes al motor de combustión, poniendo de manifiesto sus ventajas sustanciales, pero también analizando dificultades y líneas de actuación para superarlas. Los métodos desarrollados en esta Tesis Doctoral son generales y aplicables a otros criterios si se dispone de los modelos adecuados.<br>El Control Òptim (CO) és essencialment un problema matemàtic de cerca d'extrems, que consisteix en la definició d'un criteri a minimitzar (o maximitzar), restriccions que es deuen satisfer i condicions de contorn que afecten el sistema. La teoria de CO ofereix mètodes per a derivar una trajectòria de control que minimitza (o maximitza) aquest criteri.
Aquesta Tesi tracta l'aplicació del CO en automoció i especialment al motor de combustió interna. Les ferramentes necessàries són un mètode d'optimització i una representació matemàtica de la planta motriu. Per a això, es realitza una anàlisi quantitatiu dels avantatges i inconvenients dels tres mètodes d'optimització existents a la literatura: programació dinàmica, principi mínim de Pontryagin i mètodes directes. Es desenvolupen i descriuen els algoritmes per a implementar aquests mètodes així com un model de planta motriu, validat experimentalment, que inclou la dinàmica longitudinal del vehicle, models per al motor elèctric i les bateries, i un model de motor de combustió de valors mitjans.
El CO es pot utilitzar per a tres objectius diferents:
1. Control aplicat, en cas que les condicions de contorn estiguen definides. Es pot aplicar al control del motor de combustió per a un cicle de conducció particular, traduint-se en un problema matemàtic de grans dimensions. S'estudien dos casos particulars: la gestió d'un sistema d'EGR de doble llaç, i el control complet del motor, particularment de les consignes d'injecció, SOI, EGR i VGT.
2. Obtenció de regles de control quasi-òptimes, aplicables als casos on no totes les pertorbacions són conegudes. A aquest respecte, s'analitzen el càlcul de calibratges específics de motor per a un cicle, i la gestió energètica d'un vehicle híbrid mitjançant un control estocàstic en bucle tancat.
3. Utilització de trajectòries de CO com comparativa o referència per a tasques de disseny i millora, oferint un criteri objectiu. La llei de combustió així com el dimensionament d'una planta motriu híbrida s'optimitzen mitjançant l'ús de CO.
Les estratègies de CO han sigut aplicades experimentalment als treballs referents al motor de combustió, manifestant els seus substancials avantatges, però també analitzant dificultats i línies d'actuació per superar-les. Els mètodes desenvolupats a aquesta Tesi Doctoral són generals i aplicables a uns altres criteris si es disposen dels models adequats.<br>Reig Bernad, A. (2017). Optimal Control for Automotive Powertrain Applications [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/90624<br>TESIS
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Loxton, Ryan Christopher. "Optimal control problems involving constrained, switched, and delay systems." Thesis, Curtin University, 2010. http://hdl.handle.net/20.500.11937/1479.
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In this thesis, we develop numerical methods for solving five nonstandard optimal control problems. The main idea of each method is to reformulate the optimal control problem as, or approximate it by, a nonlinear programming problem. The decision variables in this nonlinear programming problem influence its cost function (and constraints, if it has any) implicitly through the dynamic system. Hence, deriving the gradient of the cost and the constraint functions is a difficult task. A major focus of this thesis is on developing methods for computing these gradients. These methods can then be used in conjunction with a gradient-based optimization technique to solve the optimal control problem efficiently.The first optimal control problem that we consider has nonlinear inequality constraints that depend on the state at two or more discrete time points. These time points are decision variables that, together with a control function, should be chosen in an optimal manner. To tackle this problem, we first approximate the control by a piecewise constant function whose values and switching times (the times at which it changes value) are decision variables. We then apply a novel time-scaling transformation that maps the switching times to fixed points in a new time horizon. This yields an approximate dynamic optimization problem with a finite number of decision variables. We develop a new algorithm, which involves integrating an auxiliary dynamic system forward in time, for computing the gradient of the cost and constraints in this approximate problem.The second optimal control problem that we consider has nonlinear continuous inequality constraints. These constraints restrict both the state and the control at every point in the time horizon. As with the first problem, we approximate the control by a piecewise constant function and then transform the time variable. This yields an approximate semi-infinite programming problem, which can be solved using a penalty function algorithm. A solution of this problem immediately furnishes a suboptimal control for the original optimal control problem. By repeatedly increasing the number of parameters used in the approximation, we can generate a sequence of suboptimal controls. Our main result shows that the cost of these suboptimal controls converges to the minimum cost.The third optimal control problem that we consider is an applied problem from electrical engineering. Its aim is to determine an optimal operating scheme for a switchedcapacitor DC-DC power converter—an electronic device that transforms one DC voltage into another by periodically switching between several circuit topologies. Specifically, the optimal control problem is to choose the times at which the topology switches occur so that the output voltage ripple is minimized and the load regulation is maximized. This problem is governed by a switched system with linear subsystems (each subsystem models one of the power converter’s topologies). Moreover, its cost function is non-smooth. By introducing an auxiliary dynamic system and transforming the time variable (so that the topology switching times become fixed), we derive an equivalent semi-infinite programming problem. This semi-infinite programming problem, like the one that approximates the continuously-constrained optimal control problem, can be solved using a penalty function algorithm.The fourth optimal control problem that we consider involves a general switched system, which includes the model of a switched-capacitor DC-DC power converter as a special case. This switched system evolves by switching between several subsystems of nonlinear ordinary differential equations. Furthermore, each subsystem switch is accompanied by an instantaneous change in the state. These instantaneous changes—so-called state jumps—are influenced by control variables that, together with the subsystem switching times, should be selected in an optimal manner. As with the previous optimal control problems, we tackle this problem by transforming the time variable to obtain an equivalent problem in which the switching times are fixed. However, the functions governing the state jumps in this new problem are discontinuous. To overcome this difficulty, we introduce an approximate problem whose state jumps are governed by smooth functions. This approximate problem can be solved using a nonlinear programming algorithm. We prove an important convergence result that links the approximate problem’s solution with the original problem’s solution.The final optimal control problem that we consider is a parameter identification problem. The aim of this problem is to use given experimental data to identify unknown state-delays in a nonlinear delay-differential system. More precisely, the optimal control problem involves choosing the state-delays to minimize a cost function measuring the discrepancy between predicted and observed system output. We show that the gradient of this cost function can be computed by solving an auxiliary delay-differential system. On the basis of this result, the optimal control problem can be formulated—and hence solved—as a standard nonlinear programming problem.
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Rösmann, Christoph [Verfasser], Torsten [Akademischer Betreuer] Bertram, and Martin [Gutachter] Mönnigmann. "Time-optimal nonlinear model predictive control : Direct transcription methods with variable discretization and structural sparsity exploitation / Christoph Rösmann ; Gutachter: Martin Mönnigmann ; Betreuer: Torsten Bertram." Dortmund : Universitätsbibliothek Dortmund, 2019. http://d-nb.info/1199106364/34.
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Hakala, Tim. "Settling-Time Improvements in Positioning Machines Subject to Nonlinear Friction Using Adaptive Impulse Control." BYU ScholarsArchive, 2006. https://scholarsarchive.byu.edu/etd/1061.
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A new method of adaptive impulse control is developed to precisely and quickly control the position of machine components subject to friction. Friction dominates the forces affecting fine positioning dynamics. Friction can depend on payload, velocity, step size, path, initial position, temperature, and other variables. Control problems such as steady-state error and limit cycles often arise when applying conventional control techniques to the position control problem. Studies in the last few decades have shown that impulsive control can produce repeatable displacements as small as ten nanometers without limit cycles or steady-state error in machines subject to dry sliding friction. These displacements are achieved through the application of short duration, high intensity pulses. The relationship between pulse duration and displacement is seldom a simple function. The most dependable practical methods for control are self-tuning; they learn from online experience by adapting an internal control parameter until precise position control is achieved. To date, the best known adaptive pulse control methods adapt a single control parameter. While effective, the single parameter methods suffer from sub-optimal settling times and poor parameter convergence. To improve performance while maintaining the capacity for ultimate precision, a new control method referred to as Adaptive Impulse Control (AIC) has been developed. To better fit the nonlinear relationship between pulses and displacements, AIC adaptively tunes a set of parameters. Each parameter affects a different range of displacements. Online updates depend on the residual control error following each pulse, an estimate of pulse sensitivity, and a learning gain. After an update is calculated, it is distributed among the parameters that were used to calculate the most recent pulse. As the stored relationship converges to the actual relationship of the machine, pulses become more accurate and fewer pulses are needed to reach each desired destination. When fewer pulses are needed, settling time improves and efficiency increases. AIC is experimentally compared to conventional PID control and other adaptive pulse control methods on a rotary system with a position measurement resolution of 16000 encoder counts per revolution of the load wheel. The friction in the test system is nonlinear and irregular with a position dependent break-away torque that varies by a factor of more than 1.8 to 1. AIC is shown to improve settling times by as much as a factor of two when compared to other adaptive pulse control methods while maintaining precise control tolerances.
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Haus, Benedikt [Verfasser], Paolo [Akademischer Betreuer] Mercorelli, Paolo [Gutachter] Mercorelli, Benjamin [Gutachter] Klusemann, and Nils [Gutachter] Werner. "Advances in applied nonlinear control and observation methods powered by optimal filtering and disurbance compensation / Benedikt Haus ; Gutachter: Paolo Mercorelli, Benjamin Klusemann, Nils Werner ; Betreuer: Paolo Mercorelli." Lüneburg : Leuphana Universität Lüneburg, 2021. http://nbn-resolving.de/urn:nbn:de:gbv:luen4-opus4-11762.
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Anisi, David A. "Online trajectory planning and observer based control." Licentiate thesis, Stockholm : Optimization and systems theory, Royal Institute of Technology, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4153.
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Moberg, Stig. "On Modeling and Control of Flexible Manipulators." Licentiate thesis, Linköping University, Linköping University, Automatic Control, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-10463.
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<p>Industrial robot manipulators are general-purpose machines used for industrial automation in order to increase productivity, flexibility, and quality. Other reasons for using industrial robots are cost saving, and elimination of heavy and health-hazardous work. Robot motion control is a key competence for robot manufacturers, and the current development is focused on increasing the robot performance, reducing the robot cost, improving safety, and introducing new functionalities. Therefore, there is a need to continuously improve the models and control methods in order to fulfil all conflicting requirements, such as increased performance for a robot with lower weight, and thus lower mechanical stiffness and more complicated vibration modes. One reason for this development of the robot mechanical structure is of course cost-reduction, but other benefits are lower power consumption, improved dexterity, safety issues, and low environmental impact.</p><p>This thesis deals with three different aspects of modeling and control of flexible, i.e., elastic, manipulators. For an accurate description of a modern industrial manipulator, the traditional flexible joint model, described in literature, is not sufficient. An improved model where the elasticity is described by a number of localized multidimensional spring-damper pairs is therefore proposed. This model is called the extended flexible joint model. This work describes identification, feedforward control, and feedback control, using this model.</p><p>The proposed identification method is a frequency-domain non-linear gray-box method, which is evaluated by the identification of a modern six-axes robot manipulator. The identified model gives a good description of the global behavior of this robot.</p><p>The inverse dynamics control problem is discussed, and a solution methodology is proposed. This methodology is based on a differential algebraic equation (DAE) formulation of the problem. Feedforward control of a two-axes manipulator is then studied using this DAE approach.</p><p>Finally, a benchmark problem for robust feedback control of a single-axis extended flexible joint model is presented and some proposed solutions are analyzed.</p>
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Challa, Subhash. "Nonlinear state estimation and filtering with applications to target tracking problems." Thesis, Queensland University of Technology, 1998.
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Bonis, Ioannis. "Optimisation and control methodologies for large-scale and multi-scale systems." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/optimisation-and-control-methodologies-for-largescale-and-multiscale-systems(6c4a4f13-ebae-4d9d-95b7-cca754968d47).html.
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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.
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Anisi, David A. "On Cooperative Surveillance, Online Trajectory Planning and Observer Based Control." Doctoral thesis, KTH, Optimeringslära och systemteori, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-9990.
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The main body of this thesis consists of six appended papers. In the first two, different cooperative surveillance problems are considered. The second two consider different aspects of the trajectory planning problem, while the last two deal with observer design for mobile robotic and Euler-Lagrange systems respectively.In Papers A and B, a combinatorial optimization based framework to cooperative surveillance missions using multiple Unmanned Ground Vehicles (UGVs) is proposed. In particular, Paper A considers the the Minimum Time UGV Surveillance Problem (MTUSP) while Paper B treats the Connectivity Constrained UGV Surveillance Problem (CUSP). The minimum time formulation is the following. Given a set of surveillance UGVs and a polyhedral area, find waypoint-paths for all UGVs such that every point of the area is visible from a point on a waypoint-path and such that the time for executing the search in parallel is minimized. The connectivity constrained formulation extends the MTUSP by additionally requiring the induced information graph to be kept recurrently connected at the time instants when the UGVs perform the surveillance mission. In these two papers, the NP-hardness of both these problems are shown and decomposition techniques are proposed that allow us to find an approximative solution efficiently in an algorithmic manner.Paper C addresses the problem of designing a real time, high performance trajectory planner for an aerial vehicle that uses information about terrain and enemy threats, to fly low and avoid radar exposure on the way to a given target. The high-level framework augments Receding Horizon Control (RHC) with a graph based terminal cost that captures the global characteristics of the environment. An important issue with RHC is to make sure that the greedy, short term optimization does not lead to long term problems, which in our case boils down to two things: not getting into situations where a collision is unavoidable, and making sure that the destination is actually reached. Hence, the main contribution of this paper is to present a trajectory planner with provable safety and task completion properties. Direct methods for trajectory optimization are traditionally based on a priori temporal discretization and collocation methods. In Paper D, the problem of adaptive node distribution is formulated as a constrained optimization problem, which is to be included in the underlying nonlinear mathematical programming problem. The benefits of utilizing the suggested method for online trajectory optimization are illustrated by a missile guidance example.In Paper E, the problem of active observer design for an important class of non-uniformly observable systems, namely mobile robotic systems, is considered. The set of feasible configurations and the set of output flow equivalent states are defined. It is shown that the inter-relation between these two sets may serve as the basis for design of active observers. The proposed observer design methodology is illustrated by considering a unicycle robot model, equipped with a set of range-measuring sensors. Finally, in Paper F, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analyzed. This observer is a generalization of the observer proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented by a proof that the region of contraction is infinitely thin. Moreover, assuming a priori bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature.<br>QC 20100622<br>TAIS, AURES