Adaptive indirect inverse control for nonlinear systems actuated by smart-material actuator*

In this paper, by incorporating implicit inverse technique into a dynamic surface based adaptive control design framework, we have developed a robust adaptive dynamic surface implicit inverse control for a class of nonlinear systems with unknown Prandtl-Ishilinskii (PI) hysteresis. Our development one hand is to eliminate the problem of “explosion of complexity” inherent in the backstepping method, on the other hand, instead of constructing the hysteresis inverse model to eliminate the hysteresis in the system, we eliminate the hysteresis by finding the optimal value of the PI performance index. And solve the difficulty of solving the hysteresis model by optimizing the method. In addition, the stability analysis shows that the system is semi-globally consistent and ultimately bounded, and the effectiveness of the proposed method is proved by simulation results.