Title: Adaptive sliding mode control for uncertain discrete-time systems using an improved reaching law


Author: Toshio Yoshimura


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


Journal: Int. J. of Modelling, Identification and Control, 2012 Vol.16, No.4, pp.380 - 391


Abstract: This paper is concerned with the design of an adaptive sliding mode control (SMC) for uncertain discrete-time systems using an improved reaching law. It is assumed that the dynamic systems are described by a non-linear discrete-time vector state equation with uncertainties, and the states for the dynamic systems are measured by the contamination with independent random noises. The proposed adaptive SMC is composed of the equivalent and the modified switching controls, and it is designed based that the time variation of the sliding surface is expressed as a discrete-time polynomial. The estimates for the un-measurable states and the uncertainties are obtained by the proposed weighted extended Kalman filter (WEKF) using a set of the noisy measurements. It is proved that the estimation errors will converge to zero as time tends to infinite under some conditions, and that the states for the dynamic systems are ultimately bounded under the action of the proposed adaptive SMC. Through the simulation experiment in numerical examples, it is indicated that the proposed adaptive SMC more improves the system performance than the conventional adaptive SMC.


Keywords: adaptive control; sliding mode control; adaptive SMC; equivalent control; modified switching control; improved reaching law; polynomial; uncertain systems; discrete time systems; weighted extended Kalman filter; WEKF; convergence; ultimate boundedness; simulation.


DOI: http://dx.doi.org/10.1504/IJMIC.2012.048271


Available online 25 Jul 2012



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