Optimal robust control for generalized fuzzy dynamical systems: A novel use on fuzzy uncertainties

Abstract

A novel approach for optimal robust control of a class of generalized fuzzy dynamical systems is proposed. This is a novel use of fuzzy uncertainty in doing dynamical system control. The system may have nonlinear nominal terms and the other terms with uncertainty, including unknown parameters and input disturbances. The Fuzzy sets theory is creatively employed in presenting the system parameter and input uncertainty, and then the control structure is deterministic (versus if-then rule-based as is typical in Mamdani-type fuzzy control). The desired controlled system performance is also deterministic, with guaranteed performances of uniform boundedness and uniform ultimate boundedness. Fuzzy informations on the uncertainties are used in searching optimal control gain under a proposed LQG-like quadratic cost index. The control gain design problem is formulated as a constrained optimization problem with the solution be proved to be always existed and unique. Systematic procedure is summarized for such control design.