An Optimal Control Problem of Adaptive Fuzzy Controllers for Fuzzy Control Systems

Advances in nonlinear control theory have provided the mathematical foundations necessary to establish conditions for stability of adaptive fuzzy controllers. In this paper, we dedicate to fuzzy control systems with the use of Popov´s hyper-stability theory. We present a stability analysis method which provides useful information to the development of fuzzy control systems and give a comparative analysis between the adaptive fuzzy techniques and some conventional adaptive control techniques. Furthermore, we display the presence of random disturbances in the control process in order to demonstrate the validity of the hybrid modeling dynamically and determine the optimal admission policies. Meanwhile, a new mathematical model is proposed to solve the optimal problem based on computational granular framework and fuzzy partitions of involved variables, automatic fuzzy hypotheses generation and testing.