Approche Unifiée de l'Analyse et de la Commande des Systèmes par Optimisation LMI

Abstract : Convex optimization on Affine Matrix Inequality constraints (widely known as LMI) was recently used for numerous automatic control problems. Herein, a methodology is proposed, whose purpose is to get insight how an automatic control problem can be cast as an LMI based optimization problem. This methodology is based on the input/output approach. Systems are modeled as connections of sub systems; the behavior of each sub system is described by a set of quadratic inequalities and stability/performance criteria are obtained using graph separation theorem and S procedure arguments. Applying this methodology, analysis and synthesis theorems are derived, which unify previous results and leads to new one. Among the new results, we can list gain scheduled control (initial motivation of this PhD Thesis), decentralized control, control with input saturations and quadratic'' control of nonlinear rational systems and so on... Conventional robustness analysis of systems is extended to more general uncertainties. For LTI systems, a more precise description and more general performance criteria are considered due to the description of the system behavior with quadratic constraints. A possible application is the hierarchical analysis of large scale systems. Its extension to nonlinear, time varying systems is presented. In this context, an application to the analysis of systems with time varying uncertainties (with a bounded rate of variation in means) is obtained. Some of the previous results are applied to the (nonlinear) missile control. The PI controlled nonlinear system is proved to be stable and to achieve performance. A controller improving the previous control law is obtained, using gain scheduling synthesis method.
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• HAL Id : tel-00009249, version 1

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Gérard Scorletti. Approche Unifiée de l'Analyse et de la Commande des Systèmes par Optimisation LMI. Automatique / Robotique. Université Paris Sud - Paris XI, 1997. Français. ⟨tel-00009249⟩

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