Adaptive Control for Time-Varying Nonlinear Hysteresis Systems With Application to Piezoelectric Positioning Platform

The adaptive control for nonlinear systems with asymmetric hysteresis nonlinearity, time-varying parameters and unknown external disturbances is addressed in this article. First, an asymmetric shifted Prandtl–Ishlinskii model and its inverse model are introduced to characteristic asymmetric hysteresis nonlinearity. To deal with unknown time-varying parameters, dynamic systems with known inputs are introduced, and parameter adaptive laws are generated by dynamic systems. In the process of handling unknown time-varying parameter in the input path, two types of coupling terms will appear, i.e., the coupling of unknown uncertainties and unknown time-varying parameter with the control input. To address these coupling terms, a special form of control input containing the Riccati differential equation is constructed. Then, sufficient condition for the existence of a solution to the designed Riccati differential equation is given. Moreover, through Lyapunov stability analysis, we conclude that all the closed-loop signals are globally bounded. Finally, the designed control scheme is employed for the actual device, namely, the piezoelectric positioning platform. The availability of the proposed adaptive controller is tested via simulation and real experiment.