Adaptive fuzzy sliding mode control for uncertain multi-input multi-output discrete-time systems using a set of noisy measurements

This paper is concerned with the design of an adaptive fuzzy sliding mode control (AFSMC) for uncertain nonlinear multi-input multi-output (MIMO) dynamic systems using a set of noisy measurements. The dynamic systems to be considered here are described by a discrete-time nonlinear state equation with mismatched uncertainties, and the states are measured by the restriction of measurement sensors and the contamination of independent random noises. The estimates for the unmeasurable states and the uncertainties are obtained by using the weighted extended Kalman filter. In the design of the proposed AFSMC, the adaptive switching factor characterising the switching control is designed using the fuzzy inference approach where the unknown gain of the switching control is assumed to be a positive definite matrix. It is proved that under some conditions the estimation errors will converge to zero as the time tends to infinity, and the states are ultimately bounded under the action of the proposed AFSMC. The effectiveness of the proposed method is indicated through the simulation experiment of an active suspension system for a half-car model.