Rendering Optimal Design in Controlling Fuzzy Dynamical Systems: A Cooperative Game Approach

Abstract

This study investigates the robust control for uncertain dynamical systems. The uncertainty is (possibly fast) time-varying but bounded. We adopt the fuzzy set theory to describe the uncertainty in the system (hence, called the fuzzy dynamical system). A class of robust controls is proposed based on tunable parameters. The controls are deterministic and are not conventional IF–THEN fuzzy rules based (such as Mamdani type). The proposed controls are able to guarantee deterministic system performance, namely uniform boundedness and uniform ultimate boundedness. In the phase of searching for the optima from the pool of admissible control design parameters, we formulate this as a two-player cooperative game by developing two performance indexes (i.e., the cost functions), each of which is dominated by one tunable parameter (i.e., the player). By the cooperative game theory, we are able to obtain the Pareto-optimality (i.e., the optima of tunable parameters). Simulation results on an electric vehicle motion control problem are presented for demonstration.