Adaptive nonlinear regulation: equation error from the Lyapunov equation

Author

Pomet, J.-B. ; Praly, L.

Author_Institution

CAI Autom., Ecole des Mines de Paris, Fontainebleau, France

fYear

1989

fDate

13-15 Dec 1989

Firstpage

1008

Abstract

An adaptive controller for nonlinear, linearly parameterized systems is presented. The new features introduced in the design are: (1) parameter estimation is performed on the scalar Lyapunov equation instead of the n-dimensional equation of the system itself. This allows non-Lipschitz uncertainties to be tolerated, especially when the stabilizing laws are not feedback linearization plus linear control. (2) Double estimation is used. One estimate is used for the stabilizing control, and the other is used to cancel the perturbation terms introduced by the adaptation, if possible. This is proposed to solve the problem of the implicit definition of the controller which arises when one tries to do this cancellation

Keywords

Lyapunov methods; adaptive control; nonlinear control systems; parameter estimation; stability; Lyapunov equation; adaptive controller; double estimation; equation error; linearly parameterized systems; nonLipschitz uncertainties; nonlinear systems; parameter estimation; perturbation; stabilizing laws; Adaptive control; Automatic control; Computer aided instruction; Control systems; Linear feedback control systems; Nonlinear control systems; Nonlinear equations; Parameter estimation; Programmable control; Uncertainty;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1989., Proceedings of the 28th IEEE Conference on

Conference_Location

Tampa, FL

Type

conf

DOI

10.1109/CDC.1989.70276

Filename

70276