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

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.