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Pour synthétiser un correcteur robuste pour un système linéaire incertain, il existe de nombreuses méthodes linéaires. Cependant, bien souvent, le gain en robustesse se fait au détriment de la performance. Aussi, dans cette thèse, on s'intéresse à la situation où la plage des valeurs possibles des paramètres est "très grande" par rapport à la "faible" variation du niveau de performance souhaité. Dans cette situation, il peut alors s'avérer intéressant d'utiliser des correcteurs séquencés. Seulement, la mise en place de cette solution nécessite que le correcteur ait à sa disposition les paramètres sur lesquels il sera séquencé. Et il peut arriver que l'on ne souhaite pas (à cause de considérations de réalisation pratique), ou que l'on ne puisse pas disposer de la mesure de ces paramètres. On est alors amené à estimer ces paramètres et donc à utiliser le paradigme de la commande adaptative. Dans cette thèse, on cherche à proposer une méthodologie de synthèse d'un correcteur auto-adaptatif afin de résoudre un problème de commande robuste d'un procédé linéaire incertain. Après une étude théorique ayant pour objectif de proposer une telle méthodologie, le cas d'un avion instable est traité à titre d'application, permettant ainsi de mettre en évidence le bénéfice que la stratégie proposée peut apporter à la commande d'un système incertain. / Many linear methods exist to design a robust controller for an uncertain linear system. This thesis considered the situation where the range of possible values of parameters is "very large" in relation to "small" variations in the desired level of performance. Frequently, an increase in robustness is obtained at the expense of a performance loss. The use of scheduled controllers may be an innovative way to address this problem. The implementation of this solution requires the controller has at its disposal the parameters on which the scheduling is done. However, it may occur that making the measure of the parameters available is not desired (for example, because of practical implementation aspects) or not possible. In these situations, the designer of the controller is led to estimate these parameters and then to use the paradigm of adaptive control. This thesis explored a methodology for designing an adaptive controller in which to solve the problem of robust control for an uncertain linear plant. A theoretical study was first undertaken which aimed to propose such a methodology; followed by, a study of the case of an unstable airplane as an application. Such an analysis highlighted the benefits that the proposed strategy can bring to the control for an uncertain plant.

Le nombre croissant de personnes âgées dans le monde exige de relever de nouveaux défis sociétaux, notamment en termes de services d'aide et de soins de santé. Avec les récents progrès technologiques, la robotique apparaît comme une solution prometteuse pour développer des systèmes visant à faciliter et améliorer les conditions de vie de cette population. Cette thèse vise la proposition et la validation d'une approche de commande robuste et référencée intention d'une orthèse active, destinée à assister des mouvements de flexion/extension du genou pour des personnes souffrant de pathologies de cette articulation. La commande par modes glissants d'ordre 2 que nous proposons permet de prendre en compte les non-linéarités ainsi que les incertitudes paramétriques résultant de la dynamique du système équivalent orthèse-membre inférieur. Elle permet également de garantir d'une part, un bon suivi de la trajectoire désirée imposée par le thérapeute ou par le sujet lui-même, et d'autre part, une bonne robustesse vis-à-vis des perturbations externes pouvant se produire lors des mouvements de flexion/extension. Dans cette thèse, nous proposons également un modèle neuronal de type Perceptron Multi-Couches pour l'estimation de l'intention du sujet à partir de la mesure des signaux EMG caractérisant les activités musculaires volontaires du groupe musculaire quadriceps. Cette approche permet de s'affranchir d'un modèle d'activation et de contraction musculaire complexe. L'ensemble des travaux a été validé expérimentalement avec la participation volontaire de plusieurs sujets valides / The increasing number of elderly in the world reveals today new societal challenges, particularly in terms of healthcare and assistance services. With recent advances in technology, robotics appears as a promising solution to develop systems that improve the living conditions of this aging population. This thesis aims at proposing and validating an approach for robust control of an active orthosis, based on the subject intention. This orthosis is designed to assist flexion/ extension movements of the knee for people suffering from knee joint deficiencies. The proposed second order sliding mode control allows to take into account the nonlinearities and parametric uncertainties resulting from the dynamics of the equivalent lower limb-orthosis system. It also ensures on one hand, a good tracking performance of the desired trajectory imposed by the therapist or the subject itself, and on the second hand, a satisfactory robustness with respect to external disturbances that may occur during flexion and extension of the knee joint. In this thesis, a neural model based on Multi-Layer Perceptron is used to estimate the subject's intention from the measurement of the EMG signals characterizing the voluntary activities of the quadriceps muscle group. This approach overcomes the complex modeling of the muscular activation and contraction dynamics. All the proposed approaches in this thesis have been validated experimentally with the voluntary participation of several healthy subjects

Ce travail de thèse porte, en premier lieu et principalement, sur le diagnostic à base de modèle d’une classe de SLC (Systèmes Linéaires à Commutations). Une problématique récurrente dans ce type de problème concerne la prise en considération de façon explicite les deux aspects, continu et discret, constituant un SLC. Dans ce cadre, nous avons proposé une méthodologie de détection et de localisation de défauts qui combine les outils initialement dédiés au diagnostic des systèmes continus et d’autres spécifiques aux SED (Systèmes à Evénement Discrets). L’approche proposée est conçue autour de trois modules : deux types de générateurs de résidus (issus de l’Automatique continue) et un estimateur en-ligne de l’état discret, appelé diagnostiqueur (issu de l’Automatique événementielle). Notre diagnostiqueur utilise les deux types de résidus, provenant de la partie continue, afin d’identifier le mode de fonctionnement du SLC et d’isoler les défauts de capteurs. Les résidus utilisés pour la localisation des défauts de capteurs sont générés à travers un générateur développé autour d’un schéma DOS (Dedicated Observer Scheme) à base d’observateurs hybrides,à la fois robustes vis-à-vis des entrées inconnues et sensibles aux défauts de capteurs. En second lieu, sur la base des résultats obtenus à l’aide de l’approche de diagnostic développée, nous avons proposé une approche préliminaire de synthèse de lois de commande tolérantes aux défauts de capteurs stabilisante via un retour d’état. Cette approche permet de préserver les performances nominales du système (situation non défaillante)en présence d’un défaut de capteurs. L’idée consiste à reconfigurer le retour d’état en remplaçant le vecteur d’état estimé à partir d’une sortie en défaut par un autre estimé à partir d’une sortie saine. La redondance des estimations est assurée dans cette approche par un banc d’observateurs hybrides robustes qui fournit plusieurs estimations correctes des vecteurs d’état et de sorties. / This thesis focuses, in first and foremost, on the model-based diagnosis of a class of SLC (Switched Linear Systems). The basic idea is to consider the continuous and discrete aspects, forming an SLC, explicitly.In this context, we proposed a methodology for detecting and locating faults that combines the tools originally dedicated to the continuous systems and the DES (discrete event systems) diagnosis. The proposed approach is designed around three modules: two types of residual generators (from the continuous Automatic) and anon-line estimator of the discrete state, called diagnoser (from the event Automatic). Our diagnoser uses the residual generators issue from the continuous part to identify the SLC mode and isolate sensor faults.Residues used for fault location sensors are generated through a generator developed around a scheme DOS(Dedicated Observer Scheme) based on hybrid observers. These observers are robust vis-à-vis the unknown input and sensitive to sensor faults. Secondly, based on the obtained results using the previous diagnosis approach, we proposed a preliminary approach for fault-tolerant state-feedback control law synthesis. This approach preserves the nominal performance of the system (as non-defaulting) in the presence of defective sensors. The idea is to reconfigure the state feedback by replacing the state vector estimated from defected output by another estimated from non-defected one. Redundancy estimates is provided in this approach by a bank of robust hybrid observer that provides several accurate estimates of state vectors and outputs.

O objetivo do trabalho é apresentar dois algoritmos para a solução de problemas de controle ótimo quadrático robusto com restrições, dentro de um contexto de controladores preditivos (MPC do inglês Model Predictive Control). Inicialmente apresentamos uma breve introdução aos algoritmos MPC, com ênfase na abordagem do controlador linear quadrático. Em seguida são apresentados os dois algoritmos de interesse, que utilizam técnicas de otimização LMI. Dessa forma as restrições e as incertezas podem ser colocadas em formas computacionalmente tratáveis. Por fim são realizadas simulações e comparações entre esses algoritmos, bem como com técnicas de MPC encontradas na literatura atual. / The goal of the work is to present two algorithms for the solution of robust quadratic optimal control problems with restrictions, within a model predictive control (MPC) setup. Initially we present a brief introduction of the MPC algorithms, emphasizing the linear quadratic controller approach. Next the two algorithms of interest, using LMI optimization techniques, are presented. By using this technique the restrictions and uncertainties can be written in a computational way. Finally some simulations and comparisons between these algorithms, as well as with MPC techniques found in the current literature, are performed.

Colunas de destilação de alta pureza são sistemas de difícil controle. Apresentam longo tempo de resposta, comportamento altamente não linear e grande interação entre as variáveis. Os controladores preditivos são muito utilizados para o controle de colunas de destilação. Porém, em colunas de alta pureza, a incorporação de um único modelo linear geralmente acarreta em um controle de fraco desempenho. Isto pois, a representação do processo é deficiente, já que não considera variações nos ganhos e nas dinâmicas, típicas de um comportamento não linear. Estas incertezas podem, inclusive, provocar a instabilidade do controle o que resultaria em produtos que não atendam à especificação. Este trabalho tem por objetivo avaliar o desempenho dos controladores de horizonte de predição infinito com um modelo interno e com múltiplos modelos tendo o HYSYS(TM) como simulador de uma coluna de separação benzeno/tolueno e o MATLAB(TM) como ambiente para o controle supervisório. Observa-se que o controlador com apenas um modelo não é capaz de estabilizar o processo para perturbação nos valores de referência das variáveis controladas, ao contrário do controlador com múltiplos modelos. / High-purity distillation columns are systems which are typically difficult to control. The main reason for this is a strongly nonlinear and interactive system associated with a very sluggish response. Model Predictive Control is widely used for control of distillation columns. However, for high-purity columns, the use of a single linear model in the controller usually leads to a poor performance of the control system. The reason for this is the poor system representation, since variation in the system gains and time constants are not taken into account in the computation of the control law. Model uncertainties can produce instability in the control system and consequent deterioration of the product quality. The goal of this work is to evaluate the performance of infinite horizon MPC with a single internal model and with multiple models. HYSYS(TM) is used as simulator for the benzene/toluene column, and MATLAB(TM) is used as a platform for supervisory control. It is observed that the controller with a single model is not capable of stabilizing the process for disturbance in the set point of the controlled variables. Opposite to that behavior the controller with multiple models has a good performance.

Escavadeiras hidráulicas são máquinas versáteis, amplamente utilizadas na construção civil e mineração. Máquinas melhores, mais produtivas, eficientes e que oferecem segurança ao operador são uma demanda constante da indústria. Devido a estes fatores, o controle para a automação de uma escavadeira hidráulica tem sido investigado. Este estudo tem o seu foco voltado para o controle do manipulador do equipamento, que é considerado como um dos elementos fundamentais para o desenvolvimento de uma escavadeira automática. Para desenvolver um sistema de controle viável, primeiramente, foi realizado a modelagem matemática dos subsistemas mecânico e hidráulico do manipulador; posteriormente esses modelos foram acoplados para representar a interação dos subsistemas. Todos os modelos desenvolvidos foram comparados com modelos de referência, obtidos a partir de softwares comerciais dedicados a modelagem de sistema dinâmicos. Tendo sido verificado a capacidade de representação física dos modelos, a fase de projeto do controlador para o manipulador foi iniciada. Para que o controlador seja eficiente, este deve ter duas propriedades essenciais: robustez para lidar com as incertezas e distúrbios severos, e adaptabilidade para lidar com um ambiente de operação altamente dinâmico. A fim de projetar um controlador que considera a dinâmica de cada subsistema do manipulador, a técnica de controle em cascata foi adotada. Esta consiste em dividir o sistema global em subsistemas, de tal forma que seja possível projetar um controlador para cada subsistema. Devido à complexidade do modelo matemático, técnicas avançadas de controle linear e não linear foram combinadas no projeto dos controladores dos subsistemas. O controlador sintetizado foi testado através de simulação numérica, em ambiente MATLAB/Simulink®, na execução de um ciclo completo de trabalho pelo manipulador. Os resultados obtidos foram considerados satisfatórios, mesmo na presença de incertezas, distúrbios severos e de ruídos. Posteriormente, na comparação desses resultados com os de outros controladores, ficou claro que o melhor desempenho foi obtido com o controlador proposto. Isto indica a possível aplicabilidade de tal controlador para a automação deste tipo de equipamento. / Hydraulic excavators are versatile machines, widely used in civil construction and in mining. Better, more productive, and efficient machines that offer operator safety are a constant industry demand. Due to these factors, the control for the automation of a hydraulic excavator has been investigated. This study focuses on the control of the equipment\'s manipulator, which is considered as one of the fundamental elements for the development of an automatic excavator. To develop a viable control system, first, the mathematical modeling of the mechanical and hydraulic subsystems of the manip-ulator was carried out; later these models were coupled to represent the interaction between the subsystems. All the developed models were compared with reference models, obtained from a commercial software dedicated to dynamic system modeling. Having verified the physical representation capacity of the analytical models, the de-sign phase of the controller was started. For the controller to be efficient, it must have two essential properties: robustness to deal with severe uncertainties and disturb-ances, and adaptability to handle a highly dynamic operating environment. To design a controller that considers the dynamics of each subsystem of the manipulator, the cascade control technique was adopted. This consists of dividing the global system into subsystems, in such a way that it is possible to design a controller for each sub-system. Due to the complexity of the mathematical model, advanced linear and non-linear control techniques were combined in subsystem controllers design. The synthe-sized controller was tested by numerical simulation, in MATLAB/Simulink® environ-ment, in the execution of a complete work operation by the manipulator. The results obtained were considered satisfactory, even in the presence of uncertainties, severe disturbances and noise. Subsequently, in the comparison of these results with those of others controllers, it was clear that the best performance was obtained with the pro-posed controller. This indicates the possible applicability of such a controller to the automation of this type of equipment.

Despite the fact that significant progress has been made on the research of these two problems for nonlinear systems for over two decades, many problems are still open. In particular, so far the output regulation problem is mainly handled by robust control approach. This approach has certain fundamental limitations and cannot handle the following three cases. (1) The control direction is unknown. (2) The boundaries of system uncertainties are unknown. (3) The exosystem is not known precisely. / Stabilization and output regulation are two fundamental control problems. The output regulation problem aims to design a feedback controller to achieve asymptotic tracking of a class of reference inputs and rejection of a class of disturbances in an uncertain system while maintaining the internal stability of the closed-loop system. Thus the output regulation problem is more demanding than the stabilization problem. Nevertheless, under some assumptions, the output regulation problem can be converted into a stabilization problem for a well defined augmented system and the solvability of the stabilization problem for this augmented system implies that of the output regulation problem for the original plant. Therefore, to a large extent, the study of the stabilization problem will also lay a foundation for that of the output regulation problem. / To handle these problems and overcome the shortcomings of the robust control approach, in this thesis, we have incorporated the adaptive control approach with the robust control approach. Both stabilization problem and output regulation problem are considered for two important classes of nonlinear systems, namely, the output feedback systems and lower triangular systems. The main contributions are summarized as follows. (1) The adaptive output regulation problem for nonlinear systems in output feedback form is addressed without knowing the control direction. The Nussbaum gain technique is incorporated with the robust control technique to handle the unknown control direction and the nonlinearly parameterized uncertainties in the system. To overcome the dilemma caused by the unknown control direction and the nonlinearly parameterized uncertainties, we have adopted a Lyapunov direct method to solve the adaptive output regulation problem. (2) The adaptive stabilization problem for nonlinear systems in lower triangular form is solved when both static and dynamic uncertainties are present and the control direction is unknown. Technically, the presence of dynamic uncertainty has made the stabilization problem more difficult than the previous work. We have managed to combine the changing supply rate technique and the Nussbaum gain technique to deal with this difficulty. The result is also applied to solve the output regulation problem for lower triangular systems with unknown control direction. (3) The adaptive output regulation problem for nonlinear systems in output feed-back form with unknown exosystem is studied. The adaptive control technique is applied to estimate the unknown parameter results from the unknown exosystem. The condition under which the parameter estimation converges to its real value is also discussed. Further, the global disturbance rejection problem for nonlinear systems in lower triangular form is solved by formulating the unknown external disturbance as a signal produced by an unknown exosystem. (4) The theoretical results have been applied to several typical control systems leading to the solution of some long standing open problems. Some exemplified applications are: (a) Global adaptive stabilization of Chua's circuit without knowing the control direction; (b) Global output synchronization of the Chua's circuit and the harmonic system; (c) Global adaptive disturbance rejection problem of the Duffing's system with all parameters unknown; (d) Global adaptive output regulation of Van der Pol oscillator with an uncertain exosystem. / Liu, Lu. / Adviser: Jie Huang. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3693. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 204-214). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

In modern cyber-physical systems (CPSs) where the control signals are generally transmitted via shared communication networks, there is a desire to balance the closed-loop control performance with the communication cost necessary to achieve it. In this context, aperiodic real-time scheduling of control tasks comes into being and has received increasing attention recently. It is well known that model predictive control (MPC) is currently widely utilized in industrial control systems and has greatly increased profits in comparison with the proportional integral-derivative (PID) control. As communication and networks play more and more important roles in modern society, there is a great trend to upgrade and transform traditional industrial systems into CPSs, which naturally requires extending conventional MPC to communication-efficient MPC to save network resources. Motivated by this fact, we in this thesis propose robust MPC and scheduling co-design algorithms to networked CPSs possibly affected by both parameter uncertainties and additive disturbances. In Chapter 2, a dynamic event-triggered robust tube-based MPC for constrained linear systems with additive disturbances is developed, where a time-varying pre-stabilizing gain is obtained by interpolating multiple static state feedbacks and the interpolating coefficient is determined via optimization at the time instants when the MPC-based control is triggered. The original constraints are properly tightened to achieve robust constraint optimization and a sequence of dynamic sets used to test events are derived according to the optimized coefficient. We theoretically show that the proposed algorithm is recursively feasible and the closed-loop system is input-to-state stable (ISS) in the attraction region. Numerical results are presented to verify the design. In Chapter 3, a self-triggered min-max MPC strategy is developed for constrained nonlinear systems subject to both parametric uncertainties and additive disturbances, where the robust constraint satisfaction is achieved by considering the worst case of all possible uncertainty realizations. First, we propose a new cost function that relaxes the penalty on the system state in a time period where the controller will not be invoked. With this cost function, the next triggering time instant can be obtained at current time instant by solving a min-max optimization problem where the maximum triggering period becomes a decision variable. The proposed strategy is proved to be input-to-state practical stable (ISpS) in the attraction region at triggering time instants under some standard assumptions. Extensions are made to linear systems with additive disturbances, for which the conditions reduce to a linear matrix inequality (LMI). Comprehensive numerical experiments are performed to verify the correctness of the theoretical results. / Graduate