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Conference Papers Year : 2008

Uniform global asymptotic stability of adaptively controlled nonlinear systems via strict Lyapunov functions

Abstract

We study a class of adaptive tracking control problems under persistency of excitation that implies both asymptotic tracking and parameter identification. We prove uniform global asymptotic stability of the adaptively controlled dynamics by explicitly constructing a strict Lyapunov function from a nonstrict one. We then allow time varying uncertainty in the unknown parameters, and construct input-to-state stable Lyapunov functions under suitable bounds on the uncertainty and an affine growth assumption on the regressor. This allows us to quantify the effects of uncertainties on both the tracking and parameter estimation errors. We illustrate our results on the Rossler system.
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Dates and versions

hal-00857835 , version 1 (04-09-2013)

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Frédéric Mazenc, Marcio de Queiroz, Michael Malisoff. Uniform global asymptotic stability of adaptively controlled nonlinear systems via strict Lyapunov functions. 1. Annual Dynamic Systems and Control Conference (DSCC 2008), Oct 2008, Ann Arbor, United States. pp.471-476, ⟨10.1115/DSCC2008-2167⟩. ⟨hal-00857835⟩
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