Prescribed Adaptive Control of a Class of Nonlinear System with Asymmetric Hysteresis

Control of uncertain nonlinear systems with hysteresis nonlinearity has re-attracted much attention in recent years. However, the most of the results are for symmetric hysteresis. In this paper, focusing on the asymmetric hysteresis phenomenon described by asymmetric shifted Prandtl-Ishlinskii (ASPI) model, a prescribed adaptive method is proposed to mitigate the hysteresis effect. The main contributions lie in 1) firstly derive the analytic inverse compensation error of the ASPI model; 2) employ the prescribed adaptive control approach to achieve global stability of the nonlinear system and guarantee the transient and steady-state performance of the tracking error without knowledge of system parameters. Simulation results validate the effectiveness of the proposed approach.