Robust Control for Fuzzy Dynamical Systems: Uniform Ultimate Boundedness and Optimality

We propose a new approach for the control design of fuzzy dynamical systems. The system may contain uncertainty, which includes unknown parameter and input disturbance. The uncertainty lies within a prescribed fuzzy set. The control structure is deterministic, and, hence, not if-then rule-based. The desired controlled system performance includes uniform boundedness and uniform ultimate boundedness. In addition, we propose a quadratic cost index, which reflects the fuzzy system performance. We then formulate a control parameter design problem as a constrained optimization problem. It is proven that the global solution to this problem always exists and is unique. The closed-form solution and the closed-form minimum cost are derived.