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This thesis is concerned with suboptimal adaptive control of discrete linear stochastic processes whose parameters are unknown. The suboptimal adaptive controllers considered are (i) Open Loop Feedback Optimal (OLFO) controller, (ii) self-tuning controller, and (iii) optimal k step ahead controller. Two more controllers, certainty about parameter (CAP) controller and no learning (NOL) controller, that provide bounds on the performance of these adaptive controllers are also considered. Performance of these controllers have been evaluated for a first order process through monte-carlo simulations. Simulation of OLFO controller together with the bounding controllers for the first order process when there is only one unknown parameter revealed that OLFO controller is unsuitable to control unstable processes and would be an unwise choice even for controlling stable processes. Selftuning and OK controllers have been simulated for the first order process with all the parameters unknown. Three cases for the unknown parameters have been considered. They are: (i) constant unknown parameters (ii) slowly time-varying unknown parameters and (iii) rapidly time-varying unknown parameters. Simulation results showed that in certain regions of the unknown parameter space the cost produced by self tuning controller and OK controller are very similar, in certain regions the OK controller produces lesser cost than the self-tuning controller and in certain other regions both controllers perform very badly. But self-tuning controller always took only half as much computing time as OK controller. A necessary condition for convergence of OK controller to a linear constant parameter controller having the same functional form as CAP controller is found out using the ideas of uniform complete observability. For a first order process under OK controller the only occasion the condition would be violated is when there is 'turn-off'. Finally, it is shown that using the combined state/parameter estimator in the place of extended Kalman filter the computational requirement of OK controller can be reduced. For the first order process, OK controller with the combined estimator took only sixty percent as much computing time as the OK controller with extended Kalman filter without any appreciable deterioration in the performance.

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Thesis (Ph. D.)--Rutgers University, 2007. / "Graduate Program in Computer Science." Includes bibliographical references (p. 78-81).

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2008. / Includes bibliographical references (leaves 103-114). Also available in electronic version.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (M.S.)--University of Wisconsin--Madison. / Typescript. eContent provider-neutral record in process. Description based on print version record.

A thorough review of the literature on the model reduction of linear, time-invariant, dynamical systems in both the frequency and time domains is presented. Particular attention is paid to the least-squares extension of the classical method of Padé approximation. An account is given of the development of apparently different approaches of least-squares parameter- matching Padé model reduction applied to continuous-time and discrete-time systems. These approaches are shown to be related via a unifying theory. From the formulation it is possible to show several interesting features of the least-squares approach which lead to a fuller understanding of exactly how the reduced model approximates the full system. An error index is derived in the general continuous-time case and it is shown that a range of system parameter preservation options are available. Using the theory developed in the continuous-time case a non-uniqueness property of the method is proven. An ‘optimal’ least-squares method based on the approach and the introduction of weighting for the system parameters are both investigated. The unifying theory is extended to the discrete-time case where an important new stability preservation property is proved and is shown to provide the basis for a new least- squares Padé method. This method uses transformations between the z- and 5-planes to guarantee stable reduced order models approximating stable high order continuous-time systems. The application of least-squares Padé approximation is further extended to the multivariable case with particular attention given to the factors affecting the levels of order reduction achieved. Appropriate numerical examples are used to illustrate the main points of the thesis and graphs of the impulse and step responses are used throughout to visually highlight the accuracy of approximation.

Orientador: José Paulo Fernandes Garcia / Banca: Haroldo Rodrigues de Azevedo / Banca: Marcelo Carvalho M. Teixeira / Resumo: Este trabalho apresenta uma nova estratégia de controle discreto. A técnica é baseada em Modos Deslizantes Discretos, utilizando uma lei de controle suave. Quando um algoritmo de controle é implementado em um computador digital, existe um atraso no tempo de computação, devido ao tempo de execução das instruções. Neste trabalho, vamos assumir que estes atrasos são constantes e menores que um período de amostragem. A presença do atraso no tempo de computação não apenas reduz a estabilidade e robustez, mas também degrada a performance de controle. O novo controlador proposto é projetado para atuar na presença destes atrasos, melhorando substancialmente o desempenho do controle. Outra propriedade importante deste controlador é a possibilidade de trabalhar com períodos de amostragem mais altos, garantindo o uso de freqüências mais baixas de processamento, ou seja, proporcionando uma economia do hardware de atuação. A nova lei de controle proposta foi aplicada na estabilização de quatro sistemas incertos e de natureza instável: Sistema Bola e Viga, Sistema Pêndulo Invertido Linear, Sistema Pêndulo Invertido Rotacional e Sistema Pêndulo Invertido Rotacional Duplo. Resultados das simulações são apresentados e comparados com resultados de outro controlador de Modo Deslizante, proposto na literatura, caracterizando um estudo comparativo, onde a eficácia do novo controlador projetado se mostra evidente, devido a seu algoritmo de fácil elaboração prática. Para melhor visualização do comportamento dos sistemas estudados e visando a contribuição no aprendizado de sistemas de controle, modelos de animação em três dimensões foram utilizados. / Abstract: This work presents a new strategy of discrete-time control. The technique is based on Discrete-Time Sliding Modes, using a smooth control law. When a control algorithm is implemented in a digital computer, there is a computation time delay, due the execution time of the instructions. In this work, we go to assume that these delays are constant and smaller than a sampling period. The presence of the computation time delay not only reduces the stability and robustness, but also degrades the control performance. The new considered controller is projected to work in the presence of these delays, improving substantially the performance of the control. Another important property of this controller is the possibility to work with higher sampling periods, guaranteeing the use of lower frequencies of processing, providing an economy of the actuation hardware. The new control law proposal was applied in the stabilization of four uncertain systems with unstable nature: Ball and Beam System, Linear Inverted Pendulum System, Rotational Inverted Pendulum System and Double Rotational Inverted Pendulum System. Simulations results are presented and compared with results of other Sliding Mode controller, proposed in the literature, characterizing a comparative study, where the effectiveness of the new designed controller shows evident, due your algorithm of easy practical elaboration. For better visualization of the behavior of the systems studied and aiming at the contribution in the learning of control systems, models of animation in three dimensions had been used. / Mestre