Title: Adaptive sliding mode control for a class of non-linear discrete-time systems with mismatched time-varying uncertainty

Authors: Toshio Yoshimura

Addresses: The University of Tokushima, Minamijosanjima-cho 2-1, Tokushima 770-8506, Japan

Abstract: This paper is concerned with an adaptive sliding mode control (SMC) of a class of non-linear discrete-time systems with mismatched time-varying uncertainty. It is assumed that the non-linear discrete-time system is described by a state equation subject to a random disturbance, and the state is measured in the contamination with random noise. The disturbance is denoted as mismatched time-varying uncertainty, and the estimates for the state and the uncertainty are taken by using the proposed weighted least squares estimator (WLSE). The proposed adaptive SMC is constructed on the basis of the estimates obtained by the proposed WLSE. It is verified by the Lyapunov method that the estimation error equation and the non-linear discrete-time system are ultimately stable under the action of the proposed adaptive SMC. The effectiveness of the proposed method is indicated by the simulation experiment in a simple numerical example.

Keywords: nonlinear discrete-time systems; mismatched time-varying uncertainty; adaptive control; sliding mode control; SMC; sliding surface; weighted least squares estimator; WLSE; Lyapunov method.

DOI: 10.1504/IJMIC.2008.021162

International Journal of Modelling, Identification and Control, 2008 Vol.4 No.3, pp.250 - 259

Published online: 07 Nov 2008 *

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