A non-cooperative game approach to the robust control design for a class of fuzzy dynamical systems. (June 2022) - Dong, Fangfang; Jin, Dong; Zhao, Xiaomin; Han, Jiang; Lu, Wei
Abstract: Aiming at the time-varying bounded uncertainty in the mechanical system and the problem of excessive control gain caused by the "worst case", a robust control with tunable parameters that can be used to compensate for the uncertainty is proposed. The proposed control can guarantee that the system has uniform boundedness and uniform ultimate boundedness. Besides, the fuzzy set theory is used to describe the uncertainty to avoid introducing any IF-THEN fuzzy logic rules or probability theory. Based on the non-cooperative game theory, the parameters of the proposed control are optimized. We treat mutually independent parameters to be optimized as players, then design performance indexes for each parameter as its cost function, and solve the optimal result by the definition of Nash equilibrium. Finally, taking the trajectory tracking control of omnidirectional mobile platform as an example, the feasibility of the optimization method and the effectiveness of the control are verified by comparing with the other two control methods. Highlights: The uncertainty in mechanical system is described by fuzzy set theory. A robust control with exponential part to compensate the time-varying uncertainty is designed. The uniform boundedness and uniform ultimate boundedness of the system are guaranteed. The optimal parameters in the control are obtained to balance the control cost and system performance based on the non-cooperative game theory.