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

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.