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Uniform global asymptotic stability of a class of adaptively controlled nonlinear systems

Frédéric Mazenc 1, 2 Marcio de Queiroz 3 Michael Malisoff 4
1 MERE - Water Resource Modeling
CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique : UMR0729
2 ASB - Analyse des Systèmes et Biométrie
3 Department of Mechanical and Industrial Engineering [Baton Rouge]
4 LSU Mathematics - Department of Mathematics [Baton Rouge]
Abstract : We give a new explicit, global, strict Lyapunov function construction for the error dynamics for adaptive tracking control problems, under an appropriate persistency of excitation condition. We then allow time-varying uncertainty in the unknown parameters. In this case, we construct input-to-state stable Lyapunov functions under suitable bounds on the uncertainty, provided the regressor also satisfies an affine growth condition. This lets us quantify the effects of uncertainties on both the tracking and the parameter estimation. We illustrate our results using Rossler systems.
Keywords : STABILITY OF NONLINEAR SYSTEMS ADAPTIVE CONTROL INPUT-TO-STATE STABILITY LYAPUNOV FUNCTIONS UNIFORM ASYMPTOTIC STABILITY STABILITE ASYMPTOTIQUE UNIFORME STABILITE DES SYSTEMES NON LINEAIRES COMMANDE ADAPTATIVE
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https://hal.inria.fr/hal-00858529
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Submitted on : Thursday, September 5, 2013 - 3:35:40 PM
Last modification on : Wednesday, February 10, 2021 - 3:35:28 AM

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Frédéric Mazenc, Marcio de Queiroz, Michael Malisoff. Uniform global asymptotic stability of a class of adaptively controlled nonlinear systems. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2009, 54 (5), pp.1152 - 1158. ⟨10.1109/TAC.2009.2013053⟩. ⟨hal-00858529⟩

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