Dissertationen zum Thema „Distributed Moving Horizon Estimation“

Les algorithmes distribués sont dorénavant présents dans de nombreux aspects de l'Automatique avec des applications pour des systèmes multi-robots, des réseaux de capteurs, couvrant des sujets tels que la commande, l'estimation d'état, la détection de défauts, la détection et l'atténuation des cyberattaques sur les systèmes cyber-physiques, etc. En effet, les systèmes distribués sont confrontés à des problèmes tels que l'extensibilité à un grand nombre d'agents et la communication entre eux. Dans les applications de systèmes multi-agents (par exemple, flotte de robots mobiles, réseaux de capteurs), il est désormais courant de concevoir des algorithmes d'estimation d'état de manière distribuée afin que les agents puissent accomplir leurs tâches sur la base de certaines informations partagées au sein de leur voisinage. Dans le cas de missions de surveillance, un réseau de capteurs statique et à faible coût (par exemple, caméras) pourrait ainsi être déployé pour localiser de manière distribuée des intrus dans une zone donnée. Dans ce contexte, l'objectif principal de cette thèse est de concevoir des observateurs distribués pour estimer l'état d'un système dynamique (par exemple, flotte de robots intrus) avec une charge de calcul réduite tout en gérant efficacement les contraintes et les incertitudes. Cette thèse propose de nouveaux algorithmes d'estimation distribuée à horizon glissant avec une pré-estimation de type Luenberger dans la formulation du problème local résolu par chaque capteur, entraînant une réduction significative du temps de calcul, tout en préservant la précision de l'estimation. En outre, ce manuscrit propose une stratégie de consensus pour améliorer le temps de convergence des estimations entre les capteurs sous des conditions de faible observabilité (par exemple, des véhicules intrus non visibles par certaines caméras). Une autre contribution concerne l'amélioration de la convergence de l'erreur d'estimation en atténuant les problèmes de non observabilité à l'aide d'un mécanisme de diffusion de l'information sur plusieurs pas (appelé "l-step") entre voisinages. L'estimation distribuée proposée est conçue pour des scénarios réalistes de systèmes à grande échelle impliquant des mesures sporadiques (c'est-à-dire disponibles à des instants a priori inconnus). À cette fin, les contraintes sur les mesures (par exemple, le champ de vision de caméras) sont incorporées dans le problème d'optimisation à l'aide de paramètres binaires variant dans le temps. L'algorithme développé est implémenté sous le middleware ROS (Robot Operating System) et des simulations réalistes sont faites à l'aide de l'environnement Gazebo. Une validation expérimentale de la technique de localisation proposée est également réalisée pour un système multi-véhicules (SMV) à l'aide d'un réseau de capteurs statiques composé de caméras à faible coût qui fournissent des mesures sur les positions d'une flotte de robots mobiles composant le SMV. Les algorithmes proposés sont également comparés à des résultats de la littérature en considérant diverses métriques telles que le temps de calcul et la précision des estimées
Distributed algorithms have pervaded many aspects of control engineering with applications for multi-robot systems, sensor networks, covering topics such as control, state estimation, fault detection, cyber-attack detection and mitigation on cyber-physical systems, etc. Indeed, distributed schemes face problems like scalability and communication between agents. In multi-agent systems applications (e.g. fleet of mobile robots, sensor networks) it is now common to design state estimation algorithms in a distributed way so that the agents can accomplish their tasks based on some shared information within their neighborhoods. In surveillance missions, a low-cost static Sensor Network (e.g. with cameras) could be deployed to localize in a distributed way intruders in a given area. In this context, the main objective of this work is to design distributed observers to estimate the state of a dynamic system (e.g. a multi-robot system) that efficiently handle constraints and uncertainties but with reduced computation load. This PhD thesis proposes new Distributed Moving Horizon Estimation (DMHE) algorithms with a Luenberger pre-estimation in the formulation of the local problem solved by each sensor, resulting in a significant reduction of the computation time, while preserving the estimation accuracy. Moreover, this manuscript proposes a consensus strategy to enhance the convergence time of the estimates among sensors while dealing with weak unobservability conditions (e.g. vehicles not visible by some cameras). Another contribution concerns the improvement of the convergence of the estimation error by mitigating unobservability issues by using a l-step neighborhood information spreading mechanism. The proposed distributed estimation is designed for realistic large-scale systems scenarios involving sporadic measurements (i.e. available at time instants a priori unknown). To this aim, constraints on measurements (e.g. camera field of view) are embodied using time-varying binary parameters in the optimization problem. Both realistic simulations within the Robot Operating System (ROS) framework and Gazebo environment, as well as experimental validation of the proposed DMHE localization technique of a Multi-Vehicle System (MVS) with ground mobile robots are performed, using a static Sensor Network composed of low-cost cameras which provide measurements on the positions of the robots of the MVS. The proposed algorithms are compared to previous results from the literature, considering several metrics such as computation time and accuracy of the estimates

This thesis regards the problem of optimal management of water resources in inland navigation networks from a control theory perspective. In particular, the main objective to be attained consists in guaranteeing the navigability condition of the network, i.e., ensuring that the water levels are such that vessels can travel safely. More specifically, the water levels must be kept within an interval around the setpoint. Other common objectives include minimizing the operational cost and ensuring a long lifespan of the equipment. However, inland navigation networks are large-scale systems characterized by a number of features that complicate their management, namely complex dynamics, large time delays and negligible bottom slopes. In order to achieve the optimal management, the efficient control of the hydraulic structures, e.g., gates, weirs and locks, must be ensured. To this end, a control-oriented modeling approach is derived based on an existing simplified model obtained from the Saint-Venant equations. This representation reduces the complexity of the original model, provides flexibility and allows to coordinate current and delayed information in a systematic manner. However, the resulting model formulation belongs to the class of delayed descriptor systems, for which standard control and state estimation tools would need to be extended. Instead, model predictive control and moving horizon estimation can be easily adapted for this formulation, as well as being able to deal with physical and operational constraints in a natural manner. Due to the large dimensionality of inland navigation networks, a centralized implementation is often neither possible nor desirable. In this regard, non-centralized approaches are considered, decomposing the overall system in subsystems and distributing the computational burden among the local agents, each of them in charge of meeting the local objectives. Given the fact that inland navigation networks are strongly coupled systems, a distributed approach is followed, featuring a communication protocol among local agents. Despite the optimality of the computed solutions, state estimation will only be effective provided that the sensors acquire reliable data. Likewise, the control actions will only be applied correctly if the actuators are not impacted by faults. Indeed, any error can lead to an inefficient management of the system. Therefore, the last part of the thesis is concerned with the design of supervisory strategies that allow to detect and isolate faults in inland navigation networks. All the presented modeling, centralized and distributed control and state estimation and fault diagnosis approaches are applied to a realistic case study based on the inland navigation network in the north of France to validate their effectiveness.
Cette thèse contribue à répondre au problème de la gestion optimale des ressources en eau dans les réseaux de navigation intérieure du point de vue de la théorie du contrôle. Les objectifs principales à atteindre consistent à garantir la navigabilité des réseaux de voies navigables, veiller à la réduction des coûts opérationnels et à la longue durée de vie des équipements. Lors de la conception de lois de contrôle, les caractéristiques des réseaux doivent être prises en compte, à savoir leurs dynamiques complexes, des retards variables et l’absence de pente. Afin de réaliser la gestion optimale, le contrôle efficace des structures hydrauliques doit être assuré. A cette fin, une approche de modélisation orientée contrôle est dérivée. Cependant, la formulation obtenue appartient à la classe des systèmes de descripteurs retardés, pour lesquels la commande prédictive MPC et l’estimation d’état sur horizon glissant MHE peuvent être facilement adaptés à cette formulation, tout en permettant de gérer les contraintes physiques et opérationnelles de manière naturelle. En raison de leur grande dimensionnalité, une mise en œuvre centralisée n’est souvent ni possible ni souhaitable. Compte tenu du fait que les réseaux de navigation intérieure sont des systèmes fortement couplés, une approche distribuée est proposée, incluant un protocole de communication entre agents. Malgré l’optimalité des solutions, toute erreur peut entraîner une gestion inefficace du système. Par conséquent, les dernières contributions de la thèse concernent la conception de stratégies de supervision permettant de détecter et d’isoler les pannes des équipements. Toutes les approches présentées sont appliquées à une étude de cas réaliste basée sur le réseau de voies navigables du nord e la France afin de valider leur efficacité.
La present tesi versa sobre el problema de la gestió òptima dels recursos hídrics en vies de navegació interior des de la perspectiva de la teoria de control. Concretament, l’objectiu principal radica en garantir la condició de navegabilitat del s is tema. Dit d’una altra manera, es vol garantir que els nivells d’aigua siguin tals que les embarcacions puguin navegar-hi de forma segura. Aquest objectiu s’assoleix mantenint els nivells a l’interior d’un interval construït al voltant del punt d’operació. Altres objectius comuns en aquest context as piren a minimitzar els cos tos associats a l’operació dels equips, així com a prolongar-ne la seva vida útil. Ara bé, les vies de navegació interior són sistemes a gran escala caracteritzats per dinàmiques complexes, grans retards temporals i pendents negligibles, aspectes que en dificulten la gestió. Per tal d’assolir la ges tió òptima, s’ha de garantir un control eficient de les estructures hidràuliques tals com comportes, dics i rescloses. Amb aquesta finalitat, es deriva un modelat del sistema orientat a control basat en un model existent simplificat, obtingut a partir de les equacions de Saint-Venant. Aquesta nova representació redueix la complexitat del model original, proporciona flexibilitat i permet coordinar informació actual i retardada de manera sistemàtica. Malgrat això, la formulació resultant pertany a la classe de sistemes descriptors amb retard, per als quals les tècniques de control i d’estimació estàndards necessiten ser esteses. En canvi, el control predictiu basat en models i l’estimació d’estat amb horitzó lliscant es poden adaptar fàcilment a la formulació proposada. A més, són capaços de tractar amb restriccions físiques i operacionals de forma natural. Degut a les grans dimensions de les vies de navegació interior, una implementació centralitzada no resulta, tot sovint, ni possible ni desitjada. Per tal de pal·liar aquest problema, es consideren mètodes no centralitzats. D’aquesta manera, es descompon el sistema global en subsistemes i es distribueix la càrrega computacional del problema centralitzat entre els agents locals, de manera que cadascun d’ells s’encarrega de fer complir els objectius locals . En tant que les vies de navegació interior són sistemes fortament connectats, se segueix un plantejament distribuït, incloent un protocol de comunicació entre els agents locals. Malgrat la optimalitat dels resultats que les estratègies proposades puguin proporcionar, l’estimació d’estat només serà efectiva a condició que els sensors proveeixin informació fiable. Igualment, les accions de control únicament es podran aplicar correctament si els actuadors no estan afectats per fallades. En efecte, qualsevol error pot conduir a una gestió ineficaç del sistema. És per aquest motiu que la darrera part de la tes i tracta s obre el disseny d’estratègies de supervisió, que permetin detectar i aïllar fallades en vies de navegació interior. Tots els resultats de modelat, control i estimació d’es tat centralitzats i distribuïts, així com de diagnòstic de fallades, s’apliquen a un cas d’estudi realista, basat en les vies de navegació interior del nord de França, per tal de provar-ne la seva eficàcia.
La presente tesis versa sobre el problema de la gestión óptima de los recursos hídricos en vías de navegación interior desde la perspectiva de la teoría de control. En concreto, el objetivo principal consiste en garantizar la condición de navegabilidad del sistema, es decir, garantizar que los niveles de agua de los canales sean tales que las embarcaciones puedan navegar de forma segura. Dicho objetivo se consigue manteniendo los niveles dentro de un intervalo alrededor del punto de operación. Otros objetivos comunes consisten en minimizar los costes asociados a la operación de los equipos, así como a extender su vida útil. Hay que tener en cuenta que las vías de navegación interiores son sistemas a gran escala caracterizados por dinámicas complejas, grandes retardos temporales y pendientes prácticamente nulas, lo que dificulta su gestión. Para alcanzar la gestión óptima, se debe garantizar un control eficiente de las estructuras hidráulicas tales como compuertas, diques y esclusas, y para ello se deriva un modelado del sistema orientado a control, basado en un modelo simplificado ya existente, obtenido a partir de las ecuaciones de Saint-Venant. Esta nueva representación reduce la complejidad del modelo original, proporciona flexibilidad y permite coordinar información actual y retardada de forma sistemática. Sin embargo, la formulación resultante pertenece a la clase de sistemas descriptores con retardos, para los cuales las técnicas de control y de estimación de estado estándares necesitan ser extendidas. En cambio, el control predictivo basado en modelos y la estimación de estado con horizonte deslizante pueden ser fácilmente adaptadas para la formulación propuesta, además de permitir lidiar con restricciones físicas y operacionales de forma natural. Hay que tener en cuenta que, debido a las grandes dimensiones de las vías de navegación interior, una implementación centralizada no es, a menudo, ni posible ni deseada, y para paliar este problema se consideran los enfoques no centralizados. De este modo, se descompone el sistema global en subsistemas y se distribuye la carga computacional del problema centralizado entre los agentes locales, de manera que cada uno de ellos se encarga de cumplir los objetivos locales. Como las vías de navegación interior son sistemas fuertemente conectados, se sigue un enfoque distribuido, incluyendo un protocolo de comunicación entre los agentes. También se ha de considerar que la estimación de estado sólo será efectiva a condición de que los sensores provean información fiable. Asimismo, las acciones de control únicamente se podrán aplicar correctamente si los actuadores no están afectados por fallas. En efecto, cualquier avería puede conducir a una gestión ineficaz del sistema. Es por ello que la última parte de la tesis trata sobre el diseño de estrategias de supervisión que permitan detectar y aislar fallas en vías de navegación interior. Todos los resultados de modelado, control y estimación de estado centralizados y distribuidos, así como de diagnóstico de fallas, se aplican a un caso de estudio realista basado en las vías de navegación interior del norte de Francia para probar su eficacia.

Moving horizon estimation (MHE) is a class of estimation methods in which the system state and disturbance estimates are obtained by solving a constrained optimization problem. The main advantage of MHE is that information about the system can be explicitly considered in the form of constraints and hence improve the estimates. In stochastic systems the estimation error will inevitably be non-zero and the controller needs to explicitly account for it to prevent constraint violations. In order for the controller to be robustified against the estimation error, bounds on the error need to be known. These bounds can be calculated if the dynamics that govern the estimation error are known. This work presents those dynamics for the unconstrained and the constrained case of the moving horizon estimator with a linear time-invariant model, and also discusses how the bounds on the estimation error can be obtained with set-theoretical methods. Those bounds are then used for robust output-feedback model predictive control (MPC). The MHE and the MPC are derived explicitly through multi-parametric programming. The complete framework is demonstrated using simultaneous MHE and tubebased MPC. The possibility of solving MPC explicitly is very appealing for flight control of small unmanned aerial vehicles (UAVs) because the behaviour of the controller is known in advance and can be guaranteed. Flight control is a challenging task that involves a multi-layer control structure where each decision influences the other layers and the overall performance. This work investigates the requirements on the different layers and their cross-effects. A linear model of the UAV is derived such that it captures the wind which is the most challenging disturbance for UAV flight. Particular focus is placed on the design of a model predictive controller as the autopilot and on in-flight wind estimation.

The thesis work investigates brake friction estimation strategies. The friction between the brake disc and brake pads is not constant during the braking application and contributes to the amount of brake torque achieved at the wheels. In this study, it is considered that any change in the brake torque between the requested and achieved values is only due to the varying brake friction coefficient. The work gives three different approaches to estimate the brake friction coefficient using two prominent state estimation strategies, Unscented Kalman Filter and Moving Horizon Estimation. The inputs to the estimators are obtained from a Vehicle model, which is built using the wheel balance equations. The estimators have been tuned to minimize the estimation error in nominal conditions and tested for their robustness through a wide analysis, where the sensitivity of the strategies is checked against a spectra of potential system parameters and boundary conditions. Throughout all the analysis, the developed models estimate the brake friction coefficient within an acceptable error range. This work opens up opportunities for further studies that can be performed using the built estimator models.
Detta examensarbete studerar strategier för skattning av bromsfriktion. Friktionen mellan bromsskivan och bromsbeläggen är inte konstant under bromsförloppet och det är denna som genererar bromsmomentet för varje hjul. I detta arbete så antas att förändringen i bromsmoment mellan begärd och uppnått endast är på grund av varierande bromsfriktion mellan bromsbelägg och bromsskiva. Arbetet presenterar tre olika sätt att skatta bromsfriktionen genom användning av två kända skattningsmetoder, Uncented Kalman Filter och Moving Horizon Estimation. Ingående värden till skattningsmetoderna fås från en fordonsmodell som är byggd med hjälp av hjulbalansekvationer. Skattningsmetoderna har justerats så att de minimerar skattningsfelet i nominella fall och de är testade för robusthet genom en bred analys där känsligheten hos metoderna testas genom en flora av potentiella systemparametrar och gränsvärden. Genom hela analysen så uppnår de utvecklade skattningsmetoderna bromsfriktionsvärden med acceptabla felnivåer. Detta arbete öppnar upp för möjligheter för vidare analyser där de utvecklade metoderna kan användas.

L’estimation de trajectoires de débris spatiaux pendant la rentrée atmosphérique est un défi majeur pour les prochaines années, renforcé par plusieurs projets liés à l'enlèvement de débris établis par plusieurs agences spatiales. Cependant, ce problème s’avère complexe du fait des erreurs de modèle et des difficultés d’initialisation des algorithmes d’estimation induites par une mauvaise connaissance de la dynamique des débris suite à leur désintégration pendant la phase de rentrée atmosphérique. Tout estimateur choisi doit donc être robuste vis-à-vis de ces facteurs. L’estimateur à horizon glissant (MHE) est reconnu dans la littérature pour être robuste vis-à-vis d’erreurs de modèle et de mauvaise initialisation, et les travaux de thèse ont montré qu’il était adapté en termes de performances à la problématique de l’estimation des débris en phase de rentrée. En revanche, il se fonde sur une stratégie d’optimisation qui requiert de fait un temps de calcul important. Pour pallier ce problème, une nouvelle structure d’estimation à horizon glissant a été développée, impliquant un temps de calcul faible nécessaire à l’application envisagée. Cette stratégie, appelée « estimateur à horizon glissant avec pré-estimation (MHE-PE)», prend en compte les erreurs de modèle via un estimateur auxiliaire, plutôt que de chercher à obtenir les estimées du bruit d’état sur l’horizon d’estimation, comme le fait la structure de l’estimateur MHE standard. Un théorème garantissant la stabilité de la dynamique de l’erreur d’estimation du MHE-PE a par ailleurs été proposé. Enfin, les performances de cette structure dans le cadre de l’estimation en trois dimensions des trajectoires de débris pendant la phase de rentrée se sont avérées meilleures que celles observées avec des estimateurs classiques. En particulier, sans dégrader la précision et la convergence de l’estimation, l’estimateur MHE-PE requiert moins de temps de calcul du fait du nombre réduit de paramètres à optimiser
Space debris tracking during atmospheric re-entries will be a crucial challenge in the coming years, emphasized through many projects on space debris mitigation established by space agencies worldwide. However, this problem appears to be complex, due to model errors and difficulties to properly initialize the estimation algorithms, as a result of unknown dynamics of the debris and their disintegrations during the re-entries. A-to-be used estimator for this problem must be robust against these factors. The Moving Horizon Estimator (MHE) is known in the literature to be robust to model errors and bad initialization, and the PhD work has proved its ability to satisfy performances required by the debris tracking during the re-entries. However, its optimization-based framework induces a large computation time. To overcome this, a new MHE structure which requires smaller computation time than the classical MHE has been developed. This strategy, so-called “Moving Horizon Estimator with Pre-Estimation (MHE-PE)” takes into account model errors by using an auxiliary estimator rather than by searching for estimates of the process noise sequence over the horizon as in the classical strategy. A theorem which guarantees the stability of the dynamics of the estimation errors of the MHE-PE has also been proposed. Finally, performances of this structure in the context of 3D space debris tracking during the re-entries have been shown to be better than those obtained with classical estimators including the MHE. In particular, without degrading accuracy of the estimates and convergence of the estimator, the MHE-PE estimator requires smaller computation time than the MHE thanks to its small number of optimization variables

Estimating the state of a dynamic system is an essential task for achieving important objectives such as process monitoring, identification, and control. Unlike linear systems, no systematic method exists for the design of observers for nonlinear systems. Although many researchers have devoted their attention to these issues for more than 30 years, there are still many open questions. We envisage that estimation plays a crucial role in biology because of the possibility of creating new avenues for biological studies and for the development of diagnostic, management, and treatment tools. To this end, this thesis aims to address two types of nonlinear estimation techniques, namely, the high-gain observer and the moving-horizon estimator with application to three different biological plants. After recalling basic definitions of stability and observability of dynamical systems and giving a bird's-eye survey of the available state estimation techniques, we are interested in the high-gain observers. These observers may be used when the system dynamics can be expressed in specific a coordinate under the so-called observability canonical form with the possibility to assign the rate of convergence arbitrarily by acting on a single parameter called the high-gain parameter. Despite the evident benefits of this class of observers, their use in real applications is questionable due to some drawbacks: numerical problems, the peaking phenomenon, and high sensitivity to measurement noise. The first part of the thesis aims to enrich the theory of high-gain observers with novel techniques to overcome or attenuate these challenging performance issues that arise when implementing such observers. The validity and applicability of our proposed techniques have been shown firstly on a simple one-gene regulatory network, and secondly on an SI epidemic model. The second part of the thesis studies the problem of state estimation using the moving horizon approach. The main advantage of MHE is that information about the system can be explicitly considered in the form of constraints and hence improve the estimates. In this work, we focus on estimation for nonlinear plants that can be rewritten in the form of quasi-linear parameter-varying systems with bounded unknown parameters. Moving-horizon estimators are proposed to estimate the state of such systems according to two different formulations, i.e., "optimistic" and "pessimistic". In the former case, we perform estimation by minimizing the least-squares moving-horizon cost with respect to both state variables and parameters simultaneously. In the latter, we minimize such a cost with respect to the state variables after picking up the maximum of the parameters. Under suitable assumptions, the stability of the estimation error given by the exponential boundedness is proved in both scenarios. Finally, the validity of our obtained results has been demonstrated through three different examples from biological and biomedical fields, namely, an example of one gene regulatory network, a two-stage SI epidemic model, and Amnioserosa cell's mechanical behavior during Dorsal closure.

Les quadrotors sont de plus en plus présents dans notre vie quotidienne et sont utilisés dans de nombreuses applications, des services de livraison aux spectacles de drones. Beaucoup de leurs applications impliquent un contact étroit avec les humains. Si un défaut survient sur le quadrotor, notamment sur un des moteurs, cela pourrait entraîner des événements catastrophiques, des blessures et des pertes d'équipements coûteuses, voire la mort. Il est donc essentiel de se concentrer sur l'amélioration de leur sécurité et de leur fiabilité grâce à des algorithmes bien conçus qui peuvent détecter et compenser les défauts affectant les drones.Une autre source courante de défaillance des drones est de se retrouver dans une orientation difficile, telle qu'une orientation renversée, en raison de perturbations éoliennes puissantes ou d'une collision avec un mur ou un autre drone. Les contrôleurs linéaires basés sur des modèles simplifiés linéarisés autour du point de vol stationnaire et utilisant les angles d'Euler pour les représentations d'attitude sont moins susceptibles de récupérer le drone de cette orientation.L'objectif principal de cette thèse est d'améliorer la sécurité et la fiabilité des quadrotors en abordant les problèmes susmentionnés. Cela est réalisé en concevant des algorithmes de commande tolérants aux défauts qui peuvent atteindre une précision de suivi de trajectoire sous des contraintes d'actionneur et en présence de perte partielle d'actionneur et de bruit de mesure. En outre, il étend cet objectif en élaborant un algorithme qui permet de récupérer à partir d'orientations aléatoires, d'effectuer des manœuvres acrobatiques de retournement et d'atteindre un suivi de trajectoire précis, le tout en présence de défauts et de contraintes d'actionneur.Tout d'abord, la modélisation des quadrotors et plusieurs représentations d'attitude sont étudiées. Plusieurs modèles non linéaires basés sur diverses représentations d'attitude, telles que les angles d'Euler, les quaternions et les matrices de rotation, sont introduits.Un cadre de commande tolérante aux défauts actifs (AFTC) est présenté, qui intègre un module de détection et de diagnostic des défauts (FDD) basé sur un observateur non linéaire algébrique peu coûteux et un contrôleur tolérant aux défauts basé sur une commande prédictive basée sur un modèle non linéaire (NMPC). Nous pouvons ainsi atteindre une précision de suivi de trajectoire sous des contraintes d'actionneur et en présence de défauts d'actionneur.La thèse propose également un cadre de commande AFTC qui est entièrement basée sur une optimisation contrainte non linéaire. Ce cadre combine l'estimation à horizon mobile non linéaire (NMHE) en tant que module FDD et le contrôleur tolérant aux pannes basé sur la commande prédictive non linéaire (NMPC). NMHE est capable d'estimer simultanément les états et les pannes d'actionneurs à partir de mesures bruitées tout en maintenant des contraintes, ce qui permet d'obtenir un suivi de trajectoire précis en présence de pannes d'actionneurs et de mesures bruitées lorsqu'il est combiné avec le NMPC.Enfin, un nouvel algorithme de commande géométrique tolérant aux pannes est présenté. Il permet à un quadrotor de récupérer d'orientations arbitraires (drone presque renversé), d'effectuer des manœuvres acrobatiques de retournement et d'atteindre une précision de suivi de trajectoire, le tout en présence de pannes d'actionneurs et de contraintes. L'algorithme présenté démontre une performance supérieure et une sécurité et une fiabilité accrues par rapport à un contrôleur géométrique de référence issu de la littérature. Contrairement au nouvel algorithme présenté, le contrôleur de référence échoue à effectuer les mêmes missions en présence de pannes d'actionneurs. Les résultats de cette partie sont validés dans une simulation ROS-Gazebo et une preuve de concept est validée expérimentalement
Quadrotors have become increasingly present in our daily lives and are used in a wide range of applications, from delivery services to drone light shows. Many of its applications include close contact with humans. Should any fault occur to the quadrotor such on a motor, it could lead to catastrophic events, from injuries and expensive equipment loss to death. It is thus essential to focus on improving their safety and reliability through well-designed algorithms that can detect and compensate for faults affecting the drones.Another common source of drone failure is getting into a difficult orientation, such as an upside-down orientation, due to, for instance, strong wind disturbances or collision with a wall or with another drone. Linear controllers that are based on simplified models linearized around the hovering point and utilizing Euler angles for attitude representations are less likely to recover the drone from such orientation.The main objective of this thesis is to improve the safety and reliability of aerial robots by addressing the aforementioned problems. This is achieved by designing Fault-Tolerant Control (FTC) algorithms that can achieve precise trajectory tracking under actuator constraints and in the presence of partial loss of effectiveness actuator fault and measurement noise. Furthermore, it expands on this goal by devising an algorithm that allows for recovery from random orientations, performing acrobatic flip maneuvers, and achieving precise trajectory following, all in the presence of actuator faults and constraints.First, quadrotor modeling and several attitude representations are investigated. Several nonlinear models based on various attitude representations, such as Euler angles, quaternions, and rotation matrices, are introduced.Additionally, an Active Fault-Tolerant Control (AFTC) framework is presented, which integrates a fault detection and diagnosis (FDD) module based on a computationally cheap nonlinear algebraic observer and a fault-tolerant controller based on Nonlinear Model Predictive Control (NMPC). This framework can achieve precise trajectory tracking under actuator constraints and in the presence of actuator faults.The thesis also proposes an AFTC framework that is completely based on nonlinear constrained optimization. This framework combines Nonlinear Moving Horizon Estimation (NMHE) as an FDD module and NMPC as a fault-tolerant controller. NMHE is capable of simultaneously estimating states and actuator faults from noisy measurements while maintaining constraints, thus resulting in precise trajectory tracking under actuator faults and noisy measurements when combined with NMPC.Finally, a novel fault-tolerant geometric control algorithm is presented. It allows a quadrotor to recover from arbitrary orientations (almost upside-down), perform acrobatic flip maneuvers, and achieve precise trajectory tracking, all in the presence of actuator faults and constraints. The presented algorithm demonstrates superior performance and higher safety and reliability compared to a baseline geometric controller from the literature. Unlike the presented novel algorithm, the baseline controller fails to perform the same missions when under actuator faults. The results of this part are validated in a ROS-Gazebo simulation, and a proof of concept is validated through hardware experiments

The Queensland University of Technology (QUT) allows the presentation of a thesis for the Degree of Doctor of Philosophy in the format of published or submitted papers, where such papers have been published, accepted or submitted during the period of candidature. This thesis is composed of seven published/submitted papers, of which one has been published, three accepted for publication and the other three are under review. This project is financially supported by an Australian Research Council (ARC) Discovery Grant with the aim of proposing strategies for the performance control of Distributed Generation (DG) system with digital estimation of power system signal parameters. Distributed Generation (DG) has been recently introduced as a new concept for the generation of power and the enhancement of conventionally produced electricity. Global warming issue calls for renewable energy resources in electricity production. Distributed generation based on solar energy (photovoltaic and solar thermal), wind, biomass, mini-hydro along with use of fuel cell and micro turbine will gain substantial momentum in the near future. Technically, DG can be a viable solution for the issue of the integration of renewable or non-conventional energy resources. Basically, DG sources can be connected to local power system through power electronic devices, i.e. inverters or ac-ac converters. The interconnection of DG systems to power system as a compensator or a power source with high quality performance is the main aim of this study. Source and load unbalance, load non-linearity, interharmonic distortion, supply voltage distortion, distortion at the point of common coupling in weak source cases, source current power factor, and synchronism of generated currents or voltages are the issues of concern. The interconnection of DG sources shall be carried out by using power electronics switching devices that inject high frequency components rather than the desired current. Also, noise and harmonic distortions can impact the performance of the control strategies. To be able to mitigate the negative effect of high frequency and harmonic as well as noise distortion to achieve satisfactory performance of DG systems, new methods of signal parameter estimation have been proposed in this thesis. These methods are based on processing the digital samples of power system signals. Thus, proposing advanced techniques for the digital estimation of signal parameters and methods for the generation of DG reference currents using the estimates provided is the targeted scope of this thesis. An introduction to this research – including a description of the research problem, the literature review and an account of the research progress linking the research papers – is presented in Chapter 1. One of the main parameters of a power system signal is its frequency. Phasor Measurement (PM) technique is one of the renowned and advanced techniques used for the estimation of power system frequency. Chapter 2 focuses on an in-depth analysis conducted on the PM technique to reveal its strengths and drawbacks. The analysis will be followed by a new technique proposed to enhance the speed of the PM technique while the input signal is free of even-order harmonics. The other techniques proposed in this thesis as the novel ones will be compared with the PM technique comprehensively studied in Chapter 2. An algorithm based on the concept of Kalman filtering is proposed in Chapter 3. The algorithm is intended to estimate signal parameters like amplitude, frequency and phase angle in the online mode. The Kalman filter is modified to operate on the output signal of a Finite Impulse Response (FIR) filter designed by a plain summation. The frequency estimation unit is independent from the Kalman filter and uses the samples refined by the FIR filter. The frequency estimated is given to the Kalman filter to be used in building the transition matrices. The initial settings for the modified Kalman filter are obtained through a trial and error exercise. Another algorithm again based on the concept of Kalman filtering is proposed in Chapter 4 for the estimation of signal parameters. The Kalman filter is also modified to operate on the output signal of the same FIR filter explained above. Nevertheless, the frequency estimation unit, unlike the one proposed in Chapter 3, is not segregated and it interacts with the Kalman filter. The frequency estimated is given to the Kalman filter and other parameters such as the amplitudes and phase angles estimated by the Kalman filter is taken to the frequency estimation unit. Chapter 5 proposes another algorithm based on the concept of Kalman filtering. This time, the state parameters are obtained through matrix arrangements where the noise level is reduced on the sample vector. The purified state vector is used to obtain a new measurement vector for a basic Kalman filter applied. The Kalman filter used has similar structure to a basic Kalman filter except the initial settings are computed through an extensive math-work with regards to the matrix arrangement utilized. Chapter 6 proposes another algorithm based on the concept of Kalman filtering similar to that of Chapter 3. However, this time the initial settings required for the better performance of the modified Kalman filter are calculated instead of being guessed by trial and error exercises. The simulations results for the parameters of signal estimated are enhanced due to the correct settings applied. Moreover, an enhanced Least Error Square (LES) technique is proposed to take on the estimation when a critical transient is detected in the input signal. In fact, some large, sudden changes in the parameters of the signal at these critical transients are not very well tracked by Kalman filtering. However, the proposed LES technique is found to be much faster in tracking these changes. Therefore, an appropriate combination of the LES and modified Kalman filtering is proposed in Chapter 6. Also, this time the ability of the proposed algorithm is verified on the real data obtained from a prototype test object. Chapter 7 proposes the other algorithm based on the concept of Kalman filtering similar to those of Chapter 3 and 6. However, this time an optimal digital filter is designed instead of the simple summation FIR filter. New initial settings for the modified Kalman filter are calculated based on the coefficients of the digital filter applied. Also, the ability of the proposed algorithm is verified on the real data obtained from a prototype test object. Chapter 8 uses the estimation algorithm proposed in Chapter 7 for the interconnection scheme of a DG to power network. Robust estimates of the signal amplitudes and phase angles obtained by the estimation approach are used in the reference generation of the compensation scheme. Several simulation tests provided in this chapter show that the proposed scheme can very well handle the source and load unbalance, load non-linearity, interharmonic distortion, supply voltage distortion, and synchronism of generated currents or voltages. The purposed compensation scheme also prevents distortion in voltage at the point of common coupling in weak source cases, balances the source currents, and makes the supply side power factor a desired value.

Thesis (Ph. D.)--Chemical and Biomolecular Engineering, Georgia Institute of Technology, 2008.
Committee Chair: Gallivan, Martha; Committee Member: Ferguson, Ian; Committee Member: Henderson, Cliff; Committee Member: Hess, Dennis; Committee Member: Lee, Jay.

Cette thèse concerne principalement la résolution des problèmes d’inversion dynamiquedans le cadre des systèmes dynamiques non linéaires. Ainsi, un ensemble de techniquesbasées sur l’utilisation des trains de mesures passées et sauvegardées sur une fenêtreglissante, a été développé. En premier lieu, les mesures sont utilisées pour générerune famille de signatures graphiques, qui constituent un outil de classification permettantde discriminer les diverses valeurs des variables à estimer pour un système non linéairedonné. Cette première technique a été appliquée à la résolution de deux problèmes : leproblème d’électolocation d’un robot doté du sens électrique et le problème d’estimationd’état dans les systèmes à dynamiques non linéaires. Outre ces deux applications, destechniques d’inversion à horizon glissant spécifiques au problème de diagnostic des défautsd’éoliennes dans le cadre d’un benchmark international ont été développées. Cestechniques sont basées sur la minimisation de critères quadratiques basés sur des modèlesde connaissance
This thesis mainly concerns the resolution of dynamic inverse problems involvingnonlinear dynamical systems. A set of techniques based on the use of trains of pastmeasurements saved on a sliding window was developed. First, the measurements areused to generate a family of graphical signatures, which is a classification tool, in orderto discriminate between different values of variables to be estimated for a given nonlinearsystem. This technique was applied to solve two problems : the electrolocationproblem of a robot with electrical sense and the problem of state estimation in nonlineardynamical systems. Besides these two applications, receding horizon inversion techniquesdedicated to the fault diagnosis problem of a wind turbine proposed as an internationalbenchmark were developed. These techniques are based on the minimization of quadraticcriteria based on knowledge-based models

Combined sewer networks carry wastewater and storm water together. During normal operation all the water is delivered to wastewater treatment plants, where it is treated before being released to surrounding natural water bodies. However, during heavy rain events, the network capacity may become insufficient leading to untreated water discharges to the receiving environments. To mitigate these undesired effects, combined sewer networks are usually provided with detention tanks and flow redirection elements, managed to fully take advantage of the network capacity. In the last few decades automatic control techniques for the regulation of these storage and redirection elements have been developed, with real-time, global, model-based predictive ones being widely regarded as the most efficient ones due to their capacity to take advantage of instantaneous network measurements and rain intensity forecasts. In this thesis a complete methodology to develop a real-time, global, model-based predictive controller to minimize pollution effects in combined sewer networks is proposed. The physically-based model for open-channel flow is based on a set of partial differential equations, which must be solved numerically. Since in a real-time predictive control strategy the model equations must be solved many times to evaluate the effect of different control actions, the time needed to solve the equations limits the use of the physically-based model to small network instances with simple topologies. Therefore, it is a common practice to use simplified control-oriented models for real-time control. The first part of the thesis is focused on the development, calibration and validation of a simplified control-oriented model for water transport in combined sewer networks, taking into account three main features: accuracy, calibration ease and computational speed. The proposed model describes the flows through the most common elements and hydraulic structures present in combined sewer networks, some of which requiring the use of piecewise equations. Once the model equations are presented, calibration procedures to compute all the model parameters are developed. The modelling and calibration methodology is then applied to a real case study and validation results are provided. Finally, sensitivity analysis is conducted with respect to both the most relevant model parameters and the intensity of the considered rain scenarios. The second part of the thesis is devoted to model-based optimal control. First, the piecewise equations of the model are reformulated to obtain a general expression of the system by means of a set of linear equations and inequalities including continuous and binary variables. Using this general expression, matrix-based procedures for the formulation of Optimal Control Problems and State Estimation Problems are presented. Using an implementation of the case study network in a commercial sewer network simulator solving the complete physically-based model equations as virtual reality, the proposed model-based controller is evaluated. By iteratively solving State Estimation Problems and Optimal Control Problems and using the simulator to provide network measurements, a Receding Horizon Control strategy is simulated. The inclusion of State Estimation Problems in the control loop allows to perform output feedback control simulations taking into account that in a sewer network the number of available measurements is limited. Finally, a discussion of the results obtained with these simulations corresponding to different measurement availability scenarios is provided.
Les xarxes de clavegueram combinades transporten conjuntament aigües residuals i aigües pluvials. En absència de pluges, tota l'aigua és conduïda cap a plantes de tractament on és degudament tractada abans de ser retornada als cossos aquàtics adjacents. En canvi, durant episodis de pluja intensa, la capacitat de la xarxa pot esdevenir insuficient donant lloc a inundacions en zones urbanes i abocaments d'aigua no tractada als medis receptors. Per tal de mitigar aquests efectes, les xarxes de clavegueram combinades acostumen a disposar de dipòsits de retenció i elements de redistribució del cabal, regulats amb la finalitat d'aprofitar al màxim la capacitat de la xarxa. En les últimes dècades s'han desenvolupat tècniques de control automàtic per a la regulació d'aquests elements d'emmagatzematge i redistribució, essent el control a temps real, global i predictiu basat en models la tècnica considerada més eficient, donat que és capaç de tenir en compte mesures instantànies del sistema i prediccions d'intensitat de pluja. En aquesta tesi, es proposa una metodologia completa per al desenvolupament d'un controlador a temps real, global i predictiu basat en model per minimitzar els efectes contaminants en xarxes de clavegueram combinades. El model físic que descriu els fluxos en canals oberts es basa en un sistema d'equacions en derivades parcials que s'ha de resoldre numèricament. Com que en una estratègia de control predictiu a temps real les equacions del model s'han de resoldre moltes vegades per avaluar els efectes de diferents accions de control, el temps necessari per resoldre les equacions limita l'ús del model físic a xarxes petites i amb topologies simples. Per tant, és una pràctica habitual utilitzar models simplificats orientats a control per al control a temps real. La primera part de la tesi es centra en el desenvolupament, calibratge i validació d'un model simplificat orientat a control del moviment de l'aigua en xarxes de clavegueram combinades, tenint en compte tres característiques principals: la precisió, la facilitat de calibratge i la velocitat computacional. El model presentat descriu el cabal a través dels elements i estructures hidràuliques més comunes en xarxes de clavegueram combinades, algunes de les quals requereixen l'ús de funcions definides a trossos. Una vegada les equacions del model han estat presentades, es desenvolupen procediments per al calibratge de tots els paràmetres del model. La metodologia de modelat i calibratge és aleshores aplicada a un cas d'estudi corresponent a una xarxa de clavegueram real i es presenten resultats de validació. Finalment, es duu a terme una anàlisi de sensitivitat respecte als paràmetres més rellevants del model i respecte a la intensitat dels escenaris de pluja considerats. La segona part de la tesi està dedicada al control òptim basat en el model. En primer lloc, les equacions definides a trossos del model són reformulades per obtenir una expressió del sistema en termes d'un conjunt d'equacions i desigualtats lineals incloent variables contínues i binàries. Usant aquesta expressió general es presenta un procediment basat en matrius per a la formulació de problemes de Control Òptim i Estimació d'Estat. Mitjançant una implementació de la xarxa del cas d'estudi en un simulador comercial de xarxes de clavegueram que resol les equacions del model físic complet com a realitat virtual, s'avalua el controlador basat en model descrit anteriorment. Resolent iterativament problemes d'Estimació d'Estat i de Control Òptim i utilitzant el simulador per obtenir mesures, se simula una estratègia de control amb horitzó lliscant. La inclusió de problemes d'Estimació d'Estat en llaç de control permet la simulació del controlador amb output feedback, tenint en compte que el nombre de mesures disponibles en una xarxa de clavegueram és limitat. Finalment, es discuteixen els resultats obtinguts en aquestes simulacions corresponents a diferents escenaris de disponibilitat de mesures

The world's energy demand has been rapidly increasing and is projected to continue growing for at least the next two decades. With increasing global energy demand and competition from renewable energy, the oil and gas industry is striving for more efficient petroleum production. Many technical breakthroughs have enabled the drilling industry to expand the exploration to more difficult drilling such as deepwater drilling and multilateral directional drilling. For example, managed pressure drilling (MPD) offers ceaseless operation with multiple manipulated variables (MV) and wired drill pipe (WDP) provides two-way, high-speed measurements from bottom hole and along-string sensors. These technologies have maximum benefit when applied in an automation system or as a real-time advisory tool. The objective of this study is to investigate the benefit of nonlinear model-based control and estimation algorithms with various types of models. This work presents a new simplified flow model (SFM) for bottomhole pressure (BHP) regulation in MPD operations. The SFM is embedded into model-based control and estimation algorithms that use model predictive control (MPC) and moving horizon estimation (MHE), respectively. This work also presents a new Hammerstein-Wiener nonlinear model predictive controller for BHP regulation. Hammerstein-Wiener models employ input and output static nonlinear blocks before and after linear dynamics blocks to simplify the controller design. The control performance of the new Hammerstein-Wiener nonlinear controller is superior to conventional PID controllers in a variety of drilling scenarios. Conventional controllers show severe limitations in MPD because of the interconnected multivariable and nonlinear nature of drilling operations. BHP control performance is evaluated in scenarios such as drilling, pipe connection, kick attenuation, and mud density displacement and the efficacy of the SFM and Hammerstein-Wiener models is tested in various control schemes applicable to both WDP and mud pulse systems. Trusted high-fidelity drilling simulators are used to simulate well conditions and are used to evaluate the performance of the controllers using the SFM and Hammerstein-Wiener models. The comparison between non-WDP (semi-closed loop) and WDP (full-closed loop) applications validates the accuracy of the SFM under the set of conditions tested and confirms comparability with model-based control and estimation algorithms. The SFM MPC maintains the BHP within ± 1 bar of the setpoint for each investigated scenario, including for pipe connection and mud density displacement procedures that experience a wider operation range than normal drilling.

Recently, autonomous vehicles have received worldwide attentions from academic research, automotive industry and the general public. In order to achieve a higher level of automation, one of the most fundamental requirements of autonomous vehicles is the capability to respond to internal and external changes in a safe, timely and appropriate manner. Situational awareness and decision making are two crucial enabling technologies for safe operation of autonomous vehicles. This thesis presents a solution for improving the automation level of autonomous vehicles in both situational awareness and decision making aspects by utilising additional domain knowledge such as constraints and influence on a moving object caused by environment and interaction between different moving objects. This includes two specific sub-systems, model based target tracking in environmental perception module and motion planning in path planning module. In the first part, a rigorous Bayesian framework is developed for pooling road constraint information and sensor measurement data of a ground vehicle to provide better situational awareness. Consequently, a new multiple targets tracking (MTT) strategy is proposed for solving target tracking problems with nonlinear dynamic systems and additional state constraints. Besides road constraint information, a vehicle movement is generally affected by its surrounding environment known as interaction information. A novel dynamic modelling approach is then proposed by considering the interaction information as virtual force which is constructed by involving the target state, desired dynamics and interaction information. The proposed modelling approach is then accommodated in the proposed MTT strategy for incorporating different types of domain knowledge in a comprehensive manner. In the second part, a new path planning strategy for autonomous vehicles operating in partially known dynamic environment is suggested. The proposed MTT technique is utilized to provide accurate on-board tracking information with associated level of uncertainty. Based on the tracking information, a path planning strategy is developed to generate collision free paths by not only predicting the future states of the moving objects but also taking into account the propagation of the associated estimation uncertainty within a given horizon. To cope with a dynamic and uncertain road environment, the strategy is implemented in a receding horizon fashion.

Micro aerial vehicles and other autonomous systems have the potential to truly transform life as we know it, however much of the potential of autonomous systems remains unrealized because reliable navigation is still an unsolved problem with significant challenges. This dissertation presents solutions to many aspects of autonomous navigation. First, it presents ROSflight, a software and hardware architure that allows for rapid prototyping and experimentation of autonomy algorithms on MAVs with lightweight, efficient flight control. Next, this dissertation presents improvments to the state-of-the-art in optimal control of quadrotors by utilizing the error-state formulation frequently utilized in state estimation. It is shown that performing optimal control directly over the error-state results in a vastly more computationally efficient system than competing methods while also dealing with the non-vector rotation components of the state in a principled way. In addition, real-time robust flight planning is considered with a method to navigate cluttered, potentially unknown scenarios with real-time obstacle avoidance. Robust state estimation is a critical component to reliable operation, and this dissertation focuses on improving the robustness of visual-inertial state estimation in a filtering framework by extending the state-of-the-art to include better modeling and sensor fusion. Further, this dissertation takes concepts from the visual-inertial estimation community and applies it to tightly-coupled GNSS, visual-inertial state estimation. This method is shown to demonstrate significantly more reliable state estimation than visual-inertial or GNSS-inertial state estimation alone in a hardware experiment through a GNSS-GNSS denied transition flying under a building and back out into open sky. Finally, this dissertation explores a novel method to combine measurements from multiple agents into a coherent map. Traditional approaches to this problem attempt to solve for the position of multiple agents at specific times in their trajectories. This dissertation instead attempts to solve this problem in a relative context, resulting in a much more robust approach that is able to handle much greater intial error than traditional approaches.

Increasing worldwide demand for petroleum motivates greater efficiency, safety, and environmental responsibility in upstream oil and gas processes. The objective of this research is to improve these areas with advanced control methods. This work develops the integration of optimal control methods including model predictive control, moving horizon estimation, high fidelity simulators, and switched control techniques applied to subsea riser slugging and managed pressure drilling. A subsea riser slugging model predictive controller eliminates persistent offset and decreases settling time by 5% compared to a traditional PID controller. A sensitivity analysis shows the effect of riser base pressure sensor location on controller response. A review of current crude oil pipeline wax deposition prevention, monitoring, and remediation techniques is given. Also, industrially relevant control model parameter estimation techniques are reviewed and heuristics are developed for gain and time constant estimates for single input/single output systems. The analysis indicates that overestimated controller gain and underestimated controller time constant leads to better controller performance under model parameter uncertainty. An online method for giving statistical significance to control model parameter estimates is presented. Additionally, basic and advanced switched model predictive control schemes are presented. Both algorithms use control models of varying fidelity: a high fidelity process model, a reduced order nonlinear model, and a linear empirical model. The basic switched structure introduces a method for bumpless switching between control models in a predetermined switching order. The advanced switched controller builds on the basic controller; however, instead of a predetermined switching sequence, the advanced algorithm uses the linear empirical controller when possible. When controller performance becomes unacceptable, the algorithm implements the low order model to control the process while the high fidelity model generates simulated data which is used to estimate the empirical model parameters. Once this online model identification process is complete, the controller reinstates the empirical model to control the process. This control framework allows the more accurate, yet computationally expensive, predictive capabilities of the high fidelity simulator to be incorporated into the locally accurate linear empirical model while still maintaining convergence guarantees.

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

D'une manière schématique, l'optimisation dynamique de procédés consiste en trois étapes de base : (i) la modélisation, dans laquelle un modèle (phénoménologique) du procédé est construit, (ii) la formulation du problème, dans laquelle le critère de performance, les contraintes et les variables de décision sont définis, (iii) et la résolution, dans laquelle les profils optimaux des variables de décision sont déterminés. Il est important de souligner que ces profils optimaux garantissent l'optimalité pour le modèle mathématique utilisé. Lorsqu'ils sont appliqués au procédé, ces profils ne sont optimaux que lorsque le modèle décrit parfaitement le comportement du procédé, ce qui est très rarement le cas dans la pratique. En effet, les incertitudes sur les paramètres du modèle, les perturbations du procédé, et les erreurs structurelles du modèle font que les profils optimaux des variables de décision basés sur le modèle ne seront probablement pas optimaux pour le procédé. L'application de ces profils au procédé conduit généralement à la violation de certaines contraintes et/ou à des performances sous-optimales. Pour faire face à ces problèmes, l'optimisation dynamique en temps-réel constitue une approche tout à fait intéressante. L'idée générale de cette approche est d'utiliser les mesures expérimentales associées au modèle du procédé pour améliorer les profils des variables de décision de sorte que les conditions d'optimalité soient vérifiées sur le procédé (maximisation des performances et satisfaction des contraintes). En effet, pour un problème d'optimisation sous contraintes, les conditions d'optimalité possèdent deux parties : la faisabilité et la sensibilité. Ces deux parties nécessitent différents types de mesures expérimentales, à savoir les valeurs du critère et des contraintes, et les gradients du critère et des contraintes par rapport aux variables de décision. L'objectif de cette thèse est de développer une stratégie conceptuelle d'utilisation de ces mesures expérimentales en ligne de sorte que le procédé vérifie non seulement les conditions nécessaires, mais également les conditions suffisantes d'optimalité. Ce développement conceptuel va notamment s'appuyer sur les récents progrès en optimisation déterministe (les méthodes stochastiques ne seront pas abordées dans ce travail) de procédés basés principalement sur l'estimation des variables d'état non mesurées à l'aide d'un observateur à horizon glissant. Une méthodologie d'optimisation dynamique en temps réel (D-RTO) a été développée et appliquée à un réacteur batch dans lequel une réaction de polymérisation par greffage a lieu. L'objectif est de déterminer le profil temporel de température du réacteur qui minimise le temps opératoire tout en respectant des contraintes terminales sur le taux de conversion et l'efficacité de greffage
In a schematic way, process optimization consists of three basic steps: (i) modeling, in which a (phenomenological) model of the process is developed, (ii) problem formulation, in which the criterion of Performance, constraints and decision variables are defined, (iii) the resolution of the optimal problem, in which the optimal profiles of the decision variables are determined. It is important to emphasize that these optimal profiles guarantee the optimality for the model used. When applied to the process, these profiles are optimal only when the model perfectly describes the behavior of the process, which is very rarely the case in practice. Indeed, uncertainties about model parameters, process disturbances, and structural model errors mean that the optimal profiles of the model-based decision variables will probably not be optimal for the process. The objective of this thesis is to develop a conceptual strategy for using experimental measurements online so that the process not only satisfies the necessary conditions, but also the optimal conditions. This conceptual development will in particular be based on recent advances in deterministic optimization (the stochastic methods will not be dealt with in this work) of processes based on the estimation of the state variables that are not measured by a moving horizon observer. A dynamic real-time optimization (D-RTO) methodology has been developed and applied to a batch reactor where polymer grafting reactions take place. The objective is to determine the on-line reactor temperature profile that minimizes the batch time while meeting terminal constraints on the overall conversion rate and grafting efficiency

碩士
國立臺北大學
電機工程學系
106
For the topic of state estimation, estimating internal state of a dynamic system has important implications on system modeling, also a part of feedback control in control engineering. In general, the system input and output can only reflect the external features, but the dynamical system behavior needs to be described with the internal state variables. Dynamic signal has very good performance in estimation and often cited by scholars, such as traditional estimation method Klaman filter. However, thinking from a global-local trade-off, often due to the deliberate pursuit of the accuracy of the local, and lost its global system dynamic trend. This study attempted to estimate in newly developing technology ”Moving horizon estimation”, and establish a hybrid architecture with a support vector regression then build a SVR-MHE dynamic system estimation method. With the establishment of a global rough model by SVR, and then make a local dynamic estimate tracking as precise estimation. This study uses MHE to replace the Kalman filter because mainly it has four advantages. First, the ability of dynamic system tracking and estimation under implication model reference. Second, more delicate estimation ability than the Kalman filter. Third, the higher the global-local trade-off for the large-scale regularity of the system of the modeling to track and as the model based control method to improve performance. Fourth, because using SVR and encompassed a large margin against noise ability. Actually, the hybrid model is a key to dynamic system. This study will use the wind speed prediction of wind farms as an example as an experiment. Finally, a system model of longtime-distance is interpreted and re-established from the perspective of global modeling, and then applied local state estimation to estimate instantaneous wind speed at short time intervals. The simulation results of verification show that the proposed system has feasibility, and then achieves the predicted results.

Nonlinear estimation techniques play an important role for process monitoring since some states and most of the parameters cannot be directly measured. There are many techniques available for nonlinear state and parameter estimation, i.e., extended Kalman filter (EKF), unscented Kalman filter (UKF), particle filtering (PF) and moving horizon estimation (MHE) etc. However, many issues related to the available techniques are to be solved. This dissertation discusses three important techniques in nonlinear estimation, which are the application of unscented Kalman filters, improvement of moving horizon estimation via computation of the arrival cost and different implementations of extended Kalman filters. First the use of several estimation algorithms such as linearized Kalman filter (LKF), extended Kalman filter (EKF), unscented Kalman filter (UKF) and moving horizon estimation (MHE) are investigated for nonlinear systems with special emphasis on UKF as it is a relatively new technique. Detailed case studies show that UKF has advantages over EKF for highly nonlinear unconstrained estimation problems while MHE performs better for systems with constraints. Moving horizon estimation alleviates the computational burden of solving a full information estimation problem by considering a finite horizon of the measurement data; however, it is non-trivial to determine the arrival cost. A commonly used approach for computing the arrival cost is to use a first order Taylor series approximation of the nonlinear model and then apply an extended Kalman filter. The second contribution of this dissertation is that an approach to compute the arrival cost for moving horizon estimation based on an unscented Kalman filter is proposed. It is found that such a moving horizon estimator performs better in some cases than if one based on an extended Kalman filter. It is a promising alternative for approximating the arrival cost for MHE. Many comparative studies, often based upon simulation results, between extended Kalman filters (EKF) and other estimation methodologies such as moving horizon estimation, unscented Kalman filter, or particle filtering have been published over the last few years. However, the results returned by the extended Kalman filter are affected by the algorithm used for its implementation and some implementations of EKF may lead to inaccurate results. In order to address this point, this dissertation investigates several different algorithms for implementing extended Kalman filters. Advantages and drawbacks of different EKF implementations are discussed in detail and illustrated in some comparative simulation studies. Continuously predicting covariance matrix for EKF results in an accurate implementation. Evaluating covariance matrix at discrete times can also be applied. Good performance can be expected if covariance matrix is obtained from integrating the continuous-time equation or if the sensitivity equation is used for computing the Jacobian matrix.

Indiana University-Purdue University Indianapolis (IUPUI)
Moving Horizon Estimation (MHE) is a powerful estimation technique for tackling the estimation problems of the state of dynamic systems in the presence of constraints, nonlinearities and disturbances and measurement noises. In this work, the Moving Horizon Estimation approach is applied in estimating the State of Charge (SOC) and State of Health (SOH) of a battery and the results are compared against those for the traditional estimation method of Extended Kalman Filter (EKF). The comparison of the results show that MHE provides improvement in performance over EKF in terms of different state initial conditions, convergence time, and process and sensor noise variations. An equivalent circuit battery model is used to capture the dynamics of the battery states, experimental data is used to identify the parameters of the battery model. MHE based state estimation technique is applied to estimates the states of the battery model, subjected to various estimated initial conditions, process and measurement noises and the results are compared against the traditional EKF based estimation method. Both experimental data and simulations are used to evaluate the performance of the MHE. The results shows that MHE performs better than EKF estimation even with unknown initial state of the estimator, MHE converges faster to the actual states,and also MHE is found to be robust to measurement and process noises.

In this thesis, common features from the theories of open quantum systems, estimation of state dynamics and statistical mechanics have been integrated in a comprehensive framework, with the aim to analyze and quantify the energetic and information contents that can be extracted from a dynamical system subject to the external environment. The latter is usually assumed to be deleterious for the feasibility of specic control tasks, since it can be responsible for uncontrolled time-dependent (and even discontinuous) changes of the system. However, if the effects of the random interaction with a noisy environment are properly modeled by the introduction of a given stochasticity within the dynamics of the system, then even noise contributions might be seen as control knobs. As a matter of fact, even a partial knowledge of the environment can allow to set the system in a dynamical condition in which the response is optimized by the presence of noise sources. In particular, we have investigated what kind of measurement devices can work better in noisy dynamical regimes and studied how to maximize the resultant information via the adoption of estimation algorithms. Moreover, we have shown the optimal interplay between quantum dynamics, environmental noise and complex network topology in maximizing the energy transport efficiency. Then, foundational scientic aspects, such as the occurrence of an ergodic property for the system-environment interaction modes of a randomly perturbed quantum system or the characterization of the stochastic quantum Zeno phenomena, have been analyzed by using the predictions of the large deviation theory. Finally, the energy cost in maintaining the system in the non-equilibrium regime due to the presence of the environment is evaluated by reconstructing the corresponding thermodynamics entropy production. In conclusion, the present thesis can constitute the basis for an effective resource theory of noise, which is given by properly engineering the interaction between a dynamical (quantum or classical) system and its external environment.