Prompted by the desire to increase the industrial applicability range of self-tuning control, the objective of this work has been to extend the standard linear self-tuning framework to facilitate the design of self-tuning controllers for bilinear systems. Bilinear systems form a well structured class of non-linear systems within which linear systems coexist as a special subclass. They are, therefore, appropriate for modelling a wider range of processes and plant than the restrictive, yet convenient, linear model structures since such models are valid both within the linear subregion and beyond. In addition to extending the self-tuning framework for bilinear systems another significant contribution of the Thesis is the introduction of a cautious least squares estimation procedure which also enhances the existing linear self-tuning schemes.

This thesis concerns modeling and control of bilinear systems (BLS). BLS are linear but not jointly linear in state and control. In the first part of the thesis, a background to BLS and their applications to modeling and control is given. The second part, and likewise the principal theme of this thesis, is dedicated to theoretical aspects of identification, modeling and control of mainly BLS, but also linear systems. In the last part of the thesis, applications of bilinear and linear modeling and control to the activated sludge process (ASP) are given.

Novel methods of system identification are developed in this dissertation. First set of methods are designed to realize time varying linear dynamical system models from input-output experimental data. The preliminary results obtained in a recent paper by the author are extended to establish a new algorithm called the Time Varying Eigensystem Realization Algorithm (TVERA). The central aim of this algorithm is to obtain a linear, time varying, discrete time model sequence of the dynamic system directly from the input-output data. Important results relating to concepts concerning coordinate systems for linear time varying systems are developed (discrete time theory) and an intuitive understanding of equivalent realizations is provided. A procedure to develop first few time step models is detailed, providing a unified solution to the time varying identification problem. The practical problem of identifying the time varying generalized Markov parameters required for TVERA is presented as the next result. In the process, we generalize the classical time invariant input output AutoRegressive model with an eXogenous input (ARX) models to the time varying case and realize an asymptotically stable observer as a byproduct of the calculations. It is further found that the choice of the generalized time varying ARX model (GTV-ARX) can be set to realize a time varying dead beat observer. Methods to use the developed algorithm(s) in this research are then considered for application to the identification of system models that are bilinear in nature. The fact that bilinear plant models become linear for constant inputs is used in the development of an algorithm that generalizes the classical developments of Juang. An intercept problem is considered as a candidate for application of the time varying identification scheme, where departure motion dynamics model sequence is calculated about a nominal trajectory with suboptimal performance owing to the presence of unstructured perturbations. Control application is subsequently demonstrated. The dynamics of a particle in a rotating tube is considered next for identification using the time varying eigensystem realization algorithm. Continuous time bilinear system identification method is demonstrated using the particle example and the identification of an automobile brake model.

[pt] É considerado o problema de estabilidade de sistemas dinâmicos bilineares a tempo discreto em ambiente determinístico. São propostas novas condições de estabilidade para três modelos diferentes. Tais resultados são comparados com os já existentes. / [en] The stability of bilinear dynamic discrete-time systems in a deterministic environment is considered. New conditions for stability of three types of systems are proposed. The results developed here are compared with those in the current literature.

Made available in DSpace on 2014-12-17T14:54:50Z (GMT). No. of bitstreams: 1 AndersonLOC.pdf: 927541 bytes, checksum: 73019c94d2a3901e38fc25a788ef32fd (MD5) Previous issue date: 2008-10-17 / This work addresses issues related to analysis and development of multivariable predictive controllers based on bilinear multi-models. Linear Generalized Predictive Control (GPC) monovariable and multivariable is shown, and highlighted its properties, key features and applications in industry. Bilinear GPC, the basis for the development of this thesis, is presented by the time-step quasilinearization approach. Some results are presented using this controller in order to show its best performance when compared to linear GPC, since the bilinear models represent better the dynamics of certain processes. Time-step quasilinearization, due to the fact that it is an approximation, causes a prediction error, which limits the performance of this controller when prediction horizon increases. Due to its prediction error, Bilinear GPC with iterative compensation is shown in order to minimize this error, seeking a better performance than the classic Bilinear GPC. Results of iterative compensation algorithm are shown. The use of multi-model is discussed in this thesis, in order to correct the deficiency of controllers based on single model, when they are applied in cases with large operation ranges. Methods of measuring the distance between models, also called metrics, are the main contribution of this thesis. Several application results in simulated distillation columns, which are close enough to actual behaviour of them, are made, and the results have shown satisfactory / Este trabalho aborda aspectos relacionados ? an?lise e ao desenvolvimento de controladores preditivos multivari?veis baseados em multi-modelos bilineares. O Controlador Preditivo Generalizado (GPC) Monovari?vel e Multivari?vel para o caso linear ? apresentado, sendo destacadas suas propriedades, caracter?sticas principais e aplica??es na ind?stria. O GPC bilinear, que ? o controlador base de todo o desenvolvimento desta Tese, ? apresentado atrav?s da abordagem da quasilineariza??o por degrau de tempo. Alguns resultados empregando este controlador s?o apresentados de forma a evidenciar o melhor desempenho do mesmo, quando comparado ao GPC linear, visto que os modelos bilineares representam melhor a din?mica de determinados processos. A quasilineariza??o por degrau de tempo, devido ao fato de ser uma aproxima??o, provoca um erro de predi??o, que limita o desempenho deste controlador ? medida que seu horizonte de predi??o aumenta. Devido ao referido erro de predi??o, o GPC bilinear com compensa??o iterativa ? mostrado de forma a minimizar o referido erro, buscando um melhor desempenho que o GPC bilinear cl?ssico. Alguns resultados utilizando o algoritmo de compensa??o iterativa s?o mostrados. O emprego dos multi-modelos ? abordado nesta Tese, buscando suprir a defici?ncia existente em controladores baseados em modelo ?nico, quando os mesmos s?o aplicados em processos com grandes faixas de opera??o. Formas de mensura??o de dist?ncia entre modelos, tamb?m chamadas de m?tricas, consistem na principal contribui??o desta Tese. Diversos resultados de aplica??o em colunas de destila??o simuladas, que se aproximam bastante do comportamento real das mesmas, foram realizados, e os resultados se mostraram satisfat?rios

<p>This thesis concerns modeling and control of bilinear systems (BLS). BLS are linear but not jointly linear in state and control. In the first part of the thesis, a background to BLS and their applications to modeling and control is given. The second part, and likewise the principal theme of this thesis, is dedicated to theoretical aspects of identification, modeling and control of mainly BLS, but also linear systems. In the last part of the thesis, applications of bilinear and linear modeling and control to the activated sludge process (ASP) are given.</p>

Le contrôle des écoulements est un domaine en forte croissance visant à modifier un écoulement à l’aide d’actionneurs et d’algorithmes de contrôle. Un axe important du contrôle des écoulements est le contrôle des décollements car le décollement de la couche limite provoque des augmentations de traînée et donc des pertes énergétiques et des coûts en carburant. Cette thèse vise à développer des algorithmes de contrôles pour le recollement des écoulements à l’aide de jets pulsés. La première partie de cette thèse expose une technique d’identification de modèle basée sur des données expérimentales. Les modèles sont déduits de considérations physiques et de l’Automatique. Ils offrent une bonne correspondance aux données tout en restant simple et en contenant peu de coefficients. La seconde partie de cette thèse utilise ces modèles pour élaborer deux algorithmes de contrôle : le premier est un contrôle optimal en boucle ouverte et le second un contrôle robuste en boucle fermée. Ces algorithmes ont été implémentés sur diverses maquettes expérimentales (LML, ONERA, LAMIH) et leurs propriétés a été testée expérimentalement. Les tests ont été réalisés en utilisant un Arduino Uno pour les mesures et le calcul du contrôle, ce qui montre que la méthode développée est simple à appliquer et requiert peu de puissance de calcul / Flow control is a strongly growing field aiming at modifying fluid flows using actuators and control algorithms. An important part of flow control is the control of flow separation as boundary layer separation increases drag and therefore energy losses and fuel consumption. This thesis focuses on developing control algorithms for flow reattachment using pulsed jets actuators. The first part of this work develops a model identification technique based on experimental data. The models are derived from physical and control theory considerations. They provide a good fit to the data while remaining simple and using few coefficients. The second part of this work uses this models in order to design two different control algorithms : the first one is an optimal feedforward control while the second one is a robust feedback control. The control algorithms have been applied on several experimental setups (LML, ONERA, LAMIH) and their properties have been experimentally tested. The tests were conducted using a simple Arduino Uno for the measurements and computation of the control, showing that the developed method is easy to apply and requires very few computational resources

Les neurosciences computationnelles consistent en l’étude du système nerveux par la modélisation et la simulation. Plus le modèle sera proche de la réalité et plus les ressources calculatoires exigées seront importantes. La question de la complexité et de la précision est un problème bien connu dans la simulation. Les travaux de recherche menés dans le cadre de cette thèse visent à améliorer la simulation de modèles mathématiques représentant le comportement physique et chimique de récepteurs synaptiques. Les modèles sont décrits par des équations différentielles ordinaires (EDO), et leur résolution passe par des méthodes numériques. Dans le but d’optimiser la simulation, j’ai implémenté différentes méthodes de résolution numérique des EDO. Afin de faciliter la sélection du meilleur algorithme de résolution numérique, une méthode nécessitant un minimum d’information a été proposée. Cette méthode permet de choisir l’algorithme qui optimise la simulation. La méthode a permis de démontrer que la dynamique d’un modèle de récepteur synaptique influence plus les performances des algorithmes de résolution que la structure cinétique du modèle lui-même. De plus, afin de caractériser des comportements pathogènes, une phase d’optimisation est réalisée. Cependant, certaines valeurs de paramètres rendent le modèle instable. Une étude de stabilité a permis de déterminer la stabilité du modèle pour des paramètres fournis par la littérature, mais également de remonter à des contraintes de stabilité sur les paramètres. Le respect de ces contraintes permet de garantir la stabilité des modèles étudiés, et donc de garantir le succès de la procédure permettant de rendre un modèle pathogène. / Computational Neuroscience consists in studying the nervous system through modeling and simulation. It is to characterize the laws of biology by using mathematical models integrating all known experimental data. From a practical point of view, the more realistic the model, the largest the required computational resources. The issue of complexity and accuracy is a well known problem in the modeling and identification of models. The research conducted in this thesis aims at improving the simulation of mathematical models representing the physical and chemical behavior of synaptic receptors. Models of synaptic receptors are described by ordinary differential equations (ODE), and are resolved with numerical procedures. In order to optimize the performance of the simulations, I have implemented various ODE numerical resolution methods. To facilitate the selection of the best solver, a method, requiring a minimum amount of information, has been proposed. This method allows choosing the best solver in order to optimize the simulation. The method demonstrates that the dynamic of a model has greater influence on the solver performances than the kinetic scheme of the model. In addition, to characterize pathogenic behavior, a parameter optimization is performed. However, some parameter values lead to unstable models. A stability study allowed for determining the stability of the models with parameters provided by the literature, but also to trace the stability constraints depending to these parameters. Compliance with these constraints ensures the stability of the models studied during the optimization phase, and therefore the success of the procedure to study pathogen models.

Το αντικείμενο της διατριβής αφορά την ανάλυση και τον έλεγχο δυναμικών συστημάτων με περιορισμούς στο διάνυσμα της εισόδου ή/ και στις μεταβλητές κατάστασης. Τα θεωρητικά εργαλεία που χρησιμοποιήθηκαν για την εξαγωγή των αποτελεσμάτων προέρχονται από τη θεωρία ευστάθειας Lyapunov, την αρχή σύγκρισης συστημάτων και τη θεωρία συνόλων, και οδήγησαν στην εδραίωση συνθηκών ευστάθειας και την ανάπτυξη συστηματικών μεθόδων εύρεσης λύσης στο πρόβλημα ελέγχου συγκεκριμένων κατηγοριών δυναμικών συστημάτων με περιορισμούς. Πιο συγκεκριμένα, για την κατηγορία των γραμμικών συστημάτων συνεχούς και διακριτού χρόνου, προτάθηκε μια νέα μέθοδος επίλυσης του προβλήματος ευσταθειοποίησης συνόλου αρχικών συνθηκών και του υπολογισμού του μέγιστου θετικά αμετάβλητου ή αμετάβλητου με έλεγχο συνόλου παρουσία περιορισμών στις εισόδους ή/και στις καταστάσεις. Τα αποτελέσματα επεκτάθηκαν και στην κατηγορία των γραμμικών συστημάτων με πολυτοπικη αβεβαιότητα. Επίσης, μελετήθηκε η κατηγορία των αυτοανάδρομων μοντέλων κινούμενου μέσου όρου (ARMA models). Αρχικά εδραιώθηκαν συνθήκες που εγγυώνται ευστάθεια για ένα συγκεκριμένο σύνολο αρχικών συνθηκών παρουσία περιορισμών. Τα αποτελέσματα αυτά εφαρμόστηκαν στην κατηγορία των δικτυωμένων συστημάτων ελέγχου (NCS), όπου υπολογίστηκε ένας κοινός γραμμικός νόμος ελέγχου ανατροφοδότησης κατάστασης για όλο το εύρος της καθυστέρησης της εισόδου. Τέλος, μελετήθηκε η κατηγορία των διγραμμικών συστημάτων συνεχούς και διακριτού χρόνου. Αρχικά διατυπώθηκαν ικανές συνθήκες ύπαρξης πολυεδρικών συναρτήσεων Lyapunov για αυτήν την κατηγορία συστημάτων. Το πρόβλημα που μελετήθηκε είναι η ευσταθειοποίηση μιας συγκεκριμένης περιοχής του χώρου κατάστασης παρουσία περιορισμών στις εισόδους και τις καταστάσεις και προτάθηκε μια υποβέλτιστη λύση που οδηγεί στον υπολογισμό γραμμικού νόμου ελέγχου ανατροφοδότησης κατάστασης. Όλα τα αποτελέσματα προκύπτουν από την επιλογή πολυεδρικών συναρτήσεων Lyapunov οι οποίες οδηγούν στο χαρακτηρισμό πολυεδρικών εκτιμήσεων της περιοχής ελκτικότητας και θετικά αμετάβλητων συνόλων. Τα κυριότερα οφέλη της επιλογής τέτοιων συναρτήσεων είναι η μη συντηρητική εκτίμησης της περιοχή ευστάθειας και η εδράιωση συνθηκών που οδηγούν σε συστηματικές μεθόδους επίλυσης των προβλημάτων ανάλυσης και ελέγχου, η λύση των οποίων προκύπτει από τη λύση γραμμικών προβλημάτων βελτιστοποίησης. / This dissertation considers the problem of stability analysis and control of dynamical systems under constraints in the input and/or state vector. The theoretical tools used arise from Lyapunov stability theory, comparison systems theory and set theoretic methods and lead to the determination of stability conditions and development of systematic methods that solve the control problem of constrained systems of particular type. In specific, for linear discrete or continuous time systems, a novel method that leads to the solution of the initial condition set stabilization problem as well as the maximal controlled invariant set computation problem is presented. These results have been extended for the case of linear systems with polytopic uncertainty. Also, the category of auto regressive moving average (ARMA) models is investigated. First, conditions that guarantee stability for a preassigned initial conditions set for constrained ARMA models are established. These results are applied to the category of networked control systems (NCS), were a single linear state feedback control law is computed for the whole range of the input delay. Finally, the category of bilinear discrete-time or continuous-time systems is investigated. Initially, sufficient conditions which guarantee existence of polyhedral Lyapunov functions are presented. The problem studied here is the stabilization of an initial condition set in the presence of input and state constraints. The solution proposed is suboptimal and leads to the determination of a linear state feedback control law. The choice of Lyapunov functions leads to the determination of a polyhedral approximation of the domain of attraction as well as polyhedral positively invariant sets. The main benefits of choosing this type of functions is the nonconservative estimation of the domain of attraction and the establishment of stability conditions that lead to systematic control design methods through the solution of linear programming problems.

Cette thèse est dédiée à l’analyse de stabilité des systèmes non linéaires sous échantillonnage variant avec le temps. Lors de l’implémentation numérique d’un contrôleur qui est calculé en temps-continu (approche par émulation), il est d'un grand intérêt de fournir des critères de stabilité et d’estimer la borne supérieure de l’intervalle d’échantillonnage qui garantit la stabilité du système en temps discret. Plusieurs travaux récents ont abordé ces questions dans le cas de modèles linéaires, mais la question a rarement été abordée dans une étude quantitative et formelle pour les systèmes non linéaires.Tout d'abord, le mémoire présente un aperçu sur les systèmes échantillonnés. Les défis et les principales méthodes pour l'analyse de stabilité sont présentés pour le cas des systèmes linéaires invariants dans le temps et celui des systèmes non linéaires. Ensuite, l’analyse de la stabilité locale des systèmes bilinéaires échantillonnés contrôlés par un retour d'état linéaire est considérée. Deux approches sont utilisées, la première basée sur la théorie des systèmes hybrides, la seconde basée sur l’analyse des ensembles invariants contractants. Cette dernière approche est inspirée par la théorie de la dissipativité. L’ensemble de ces résultats conduisent à des conditions suffisantes de stabilité exprimées sous forme LMI.Enfin, les conditions de stabilité basées sur la dissipativité sont étendues au cas des systèmes non linéaires affines en l'entrée. Les résultats sont ensuite repris dans le cas spécifique des systèmes non linéaires polynomiaux où les conditions de stabilité sont vérifiées numériquement en utilisant la décomposition en somme des carrés (SOS). / This PhD thesis is dedicated to the stability analyzis of nonlinear systems under sampled-data control, with arbitrarily time-varying sampling intervals. When a controller is designed in continuous-time, and then implemented digitally (emulation approach), it is of great interest to provide stability criteria, and to estimate the bound on the sampling intervals which guarantees the stability of the sampled-data system. Whereas several works deal with linear models, the issue has been rarely addressed in a formal quantitative study in the nonlinear case.First, an overview on sampled-data control is presented. Challenges and main methodologies for stability analysis are presented for both the linear time-invariant and the nonlinear cases.Then, local stability of bilinear sampled-data systems controlled by a linear state feedback is considered by using two approaches: the first one is based on hybrid systems theory; the second one is based on the analyzis of contractive invariant sets and is inspired by the dissipativity theory. Both approaches provide sufficient stability conditions in the form of LMI.Finally, the dissipativity–based stability conditions are extended for the more general case of nonlinear systems which are affine in the input, including the case of polynomial systems which leads to conditions in the form of sum of squares (SOS).