Analysis and Design of Indirect Adaptive Fuzzy Controller for Nonlinear Hysteretic Systems

In order to handle the nonlinear properties of hysteretic systems, an indirect adaptive fuzzy controller (IAFC) is proposed in this paper. However, it is hard to directly identify the unknown hysteretic effects. Therefore, to overcome this problem, a dynamic hysteretic equation is employed and modified to construct the nonlinear properties of backlash-like hysteretic systems. Besides, the existence of an IAFC can be derived in this paper. Compared with the existing fuzzy control methods, our proposed IAFC is simpler and can handle the more general hysteretic problems with our new learning algorithm. Based on the learning algorithm, the adaptive and the control laws not only can be derived but the stability of the closed-loop system can also be guaranteed by the Lyapunov stability criterion. Finally, the proposed IAFC is compared to the adaptive backstepping control method, and the results show that our proposed IAFC can effectively handle the nonlinear properties in the backlash-like hysteretic systems.