Fractional robust control design for fuzzy dynamical systems: An optimal approach

We propose an optimal approach to a new control design for fuzzy dynamical systems in this paper. Consider the system containing uncertainty, which may includes the unknown system parameter and input disturbance. And the uncertainty can be prescribed with a fuzzy set. A new class of factional-type robust controls are proposed, whose structure is deterministic and is not if-then rule-based. Furthermore, the control gain design is formulated as a constrained optimization problem, which minimizes both the average fuzzy performance and control effort. We show that the solution of this optimization problem always exists and is unique. And the closed-form solution and closed-form minimum cost are derived. The resulting control can guarantee the uniform boundedness and uniform ultimate boundedness of the uncertain system, while minimizing both the average fuzzy performance and control effort.