Sur la commande adaptative des systèmes non linéaires

Jean-Baptiste Pomet 1
1 McTAO - Mathematics for Control, Transport and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This dissertation is concerned with the control of nonlinear linearly parametrlzed systems, with unknown pcrorneters, The control objective Is asymptotic stability of an equilibrlum point. The problem is : suppose you know, for each possible value of the parameters, a stabilizing control law, how to construct, from thls family of laws, an (adaptlve) stabilizing control law which does not need the exact value of the parameters? We give a general method, based on linear estimation, which results in a classification of the existing algorithrns and the design of new ones, We compare them from the followlng criterium: supposing each control law above makes the equilibrium point globally asymptotically stable, does thls globalness still hold for the adaptive control law. Compared with the existing Iiterature, we do better in two senses: we do not suppose that the known stabilizing laws are obtained via feedback linarization plus linear control, and we find some controllers giving global stability in cases when we cannot prove that the exlsting ones do so. We Introduce new ideas as estimation based on a the evolution of a Lyapunov function, or tuning the normalization from the growth of parametrlc uncertainties. Besldes, studying the posslbillty to cancel bad effects of adaptation via an a modification of the control law leads us to establlsh general conditions for feedback and/or dlffeomorphlsm equivalence of the systems of a parametrlzed family.
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Jean-Baptiste Pomet. Sur la commande adaptative des systèmes non linéaires. Automatique / Robotique. École Nationale Supérieure des Mines de Paris, 1989. Français. ⟨NNT : 1989ENMP0165⟩. ⟨pastel-00838224⟩

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