Title: Adaptive sliding mode control for non-linear discrete-time systems with mismatched 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) for non-linear discrete-time systems with mismatched uncertainty. The proposed adaptive SMC is composed of the equivalent and the switching controls, and it is constructed on the basis of the information from the proposed estimator to take the estimates for the state and uncertainty. It is assumed that some of the state variables can be measured and the uncertainty in the discrete-time systems is parameterised linearly in the unknown constant terms. The estimates for the state and the uncertainty are taken by applying the proposed weighted least squares method. It is verified based on the Lyapunov scheme according to which the estimation errors converge to zero as time increases, and the trajectory of the system response is stable as the sliding surface is suitably selected. The effectiveness of the proposed adaptive SMC is illustrated by the simulation experiment in a simple numerical example.

Keywords: discrete-time systems; mismatched uncertainty; adaptive sliding mode control; sliding surface; equivalent control; switching control; weighted least squares method; estimator; nonlinear systems.

DOI: 10.1504/IJMIC.2008.020551

International Journal of Modelling, Identification and Control, 2008 Vol.3 No.4, pp.427 - 434

Published online: 29 Sep 2008 *

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