Adaptive Control of Unknown Dynamic Hysteretic Systems

This paper first discusses the adaptive control for the hysteresis described by PrandtlIshlinskii model. Then, the adaptive control for the continuous-time linear dynamical systems preceded with hysteresis described by Prandtl-Ishlinskii model is considered. The relative degree and the upper bound of the order of the linear dynamical system are assumed to be known. The contribution of the paper is the fusion of the hysteresis model with the adaptive control techniques. Only 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 controller are adaptively estimated online. The output tracking error can be controlled to approach to zero. Simulation results show the effectiveness of the proposed algorithm.