Robust Hysteretic Observer-Based Optimal Control of Piezoelectric Nano-Motion Systems With Prescribed Performance

In this article, a robust hysteretic observer-based adaptive dynamic programming (ADP) framework is proposed to achieve both optimal performance and prescribed performance for piezoelectric nano-motion systems in the consideration of uncertain hysteresis nonlinearities and unknown external disturbances. A Bouc–Wen model is selected to characterize the behavior of the hysteresis, an extended state observer combined with a disturbance observer is constructed to simultaneously handle coupling effects between the unknown hysteretic state and the multisource disturbances. To guarantee the prescribed performance, an error transformation technique is adopted to balance transient performance and steady-state performance. With the aid of the dual observer, a robust controller is designed to compensate the hysteresis nonlinearities and various disturbances. To balance control cost and control performance, an ADP-based optimal controller is synthesized by using only an adaptive critic neural network. The Lyapunov stability theory is employed to analyze the convergence of the state observation errors, the disturbance estimation errors, and prove the stability of the closed-loop system. The performance of the hysteretic state observer and the disturbance observer is evaluated by the simulations, and the effectiveness and the superiority of the proposed control scheme are validated by comparative experimental studies deployed on a piezoelectric nano-motion stage.