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Théorie de Lyapunov, commande robuste et optimisation

Denis Arzelier 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : The field of robust control provides the theoretical principles and the numerical tools used to design engineering control systems that give adequate performance in face of uncertain environment. Since the 80s, robust multivariable control theory has developed formal methods that deal with key issues ranging from early theory of control disturbances rejection to stability and performance margins optimization. The robust control theory is built on applied mathematics (mathematical framework), operations research (optimization) and computer science (complexity theory and algorithms theory). Deeply rooted in rigorous mathematics, the aim of robust control is to develop theoretical and computational tools for versatile practical applications ranging from guidance and control of aerospace systems, to control systems for the manufacturing industries, and control of communication systems. As numerical tractability is a critical issue for realistic applications, new optimization tools are central to the development of the field. Beyond the usual relationships between both communities (optimization and control communities), a more subtle link relates the optimization theory to the control theory. Lyapunov theory, first used in an instrumental way by control practitioners, is the theoretical tool that formalizes this deep link between the two fields. Different facets of this idea are illustrated in this document. After exposing the general context of robust analysis and control as well as the particular related optimization problems, it is shown how a great number of results obtained in the framework of Lyapunov theory may be viewed as Lagrangian relaxations.
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Habilitation à diriger des recherches
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  • HAL Id : tel-00010257, version 1

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Denis Arzelier. Théorie de Lyapunov, commande robuste et optimisation. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2004. ⟨tel-00010257⟩

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