Guaranteeing Uniform Ultimate Boundedness for Uncertain Systems Free of Matching Condition

A fuzzy-based optimal approach to robust control design is proposed for interconnected uncertain systems with mismatching conditions, which were previously unavailable. The interconnected system contains uncertainty, which may include initial conditions, unknown system parameters and input disturbance. The uncertainty bound lies within a prescribed fuzzy set. The system does not satisfy the matching condition. The robust control design in this paper consists of a control scheme design and control gain optimization. A new robust control scheme is first proposed, whose structure is deterministic and not if-then fuzzy rule based. The control gain design problem is then formulated as constrained optimization by fuzzy description of the uncertainty bound, which minimizes the fuzzy system performance and the control effort. It is shown that the global solution to this optimization problem always exists and is unique. The closed-form solution and closed-form minimum cost are presented. The resulting control is able to render the system performance in twofold. First, it guarantees uniform boundedness and uniform ultimate boundedness regardless of the actual value of uncertainty. Second, it minimizes a fuzzy-based performance index. The novelty of this research is a new and carefully orchestrated effort in blending several creative methods and tools; including simultaneous state transformation and control design, dual deterministic and fuzzy features of the performance index, and raised control order; into an integrated framework, resulting in a tractable design problem.