Title: Adaptive output tracking control for a class of uncertain discrete-time systems via sliding mode theory

Authors: Toshio Yoshimura

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

Abstract: This paper is concerned with an adaptive output tracking control (AOTC) for a class of uncertain discrete-time systems via sliding mode theory. It is assumed that the uncertain discrete-time systems are described by a state equation with mismatched uncertainties found in unmodelled dynamics and external disturbances, and the uncertainties are expressed in a parameterised form. The estimates for the uncertainties are taken by using the proposed weighted least squares estimator (WLSE), and then the proposed AOTC is designed on the basis of the output from the estimator via sliding mode theory. It is verified by using the Lyapunov method that the estimation error equation is asymptotically stable and the uncertain discrete-time systems under the action of the proposed AOTC are ultimately stable. The effectiveness of the proposed method is indicated by the simulation experiment in a simple numerical example.

Keywords: adaptive output tracking control; AOTC; sliding mode theory; uncertain discrete-time system; reaching law; weighted least squares estimator; WLSE; output tracking error; Lyapunov method; ultimate stability; asymptotical stability; simulation; sliding mode control.

DOI: 10.1504/IJMIC.2008.021774

International Journal of Modelling, Identification and Control, 2008 Vol.5 No.1, pp.45 - 54

Published online: 03 Dec 2008 *

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