Adaptive control for the systems with hysteresis and uncertainties

This paper discusses the adaptive control for the uncertain discrete time linear systems preceded with hysteresis and disturbances. The contribution of the paper is the fusion of the hysteresis model with the adaptive control techniques without constructing the inverse hysteresis nonlinearity. The proposed scheme eliminates the traditional over-parameterization by only adapting the parameters (which are generated from the parameters of the linear system and the density function of the hysteresis) directly needed in the formulation of the sliding mode controller. The stability in the sense that all signals in the loop remain bounded can be guaranteed. Furthermore, if the disturbance and reference signal are slow varying with respect to the sampling frequency, the output tracking error can be controlled to be as small as required by choosing the design parameters. Simulation results show the effectiveness of the proposed algorithm.