Optimal Design of High-Order Control for Fuzzy Dynamical Systems Based on the Cooperative Game Theory.

ABSTRACT

In this article, we propose a high-order robust control for fuzzy dynamical systems. The time varying but bounded uncertainty in this system is described by the fuzzy set theory. The control is deterministic and is not based on IF-THEN fuzzy rules. By the Lyapunov approach, we prove that the control is able to guarantee uniform boundedness and uniform ultimate boundedness. In addition, the tunable parameters in the high-order control are regarded as two players in a cooperative game. Two cost functions are also proposed based on the two players. These two cost functions are related to system performance and control cost. Then, the optimal design problem is solved by finding the Pareto-optimality parameters. Numerical simulations are performed for verification.