Prescribed adaptive control of unknown hysteresis in smart material actuated systems

Design of controllers that ensure the closed-loop stability of the system actuated by the smart material which shows hysteresis nonlinearity is a challenging issue in the literature. In this paper, we use the Bouc–Wen model to describe the hysteresis nonlinearity and attempt to fuse the Bouc–Wen model with the available adaptive control techniques without constructing the inverse of the Bouc–Wen model. To realize such a fusion, it is necessary to utilize its solution properties. However, the general solution of the Bouc–Wen model is still not available. Therefore, an approximate solution is applied. By means of the approximate solution, a prescribed adaptive control approach is developed to achieve global stability of the closed-loop system and guarantee the transient and steady-state performance of the tracking error. Simulation results demonstrate the effectiveness of the proposed approach.