Optimal Robust Control Design for Constrained Uncertain Systems: A Fuzzy-Set Theoretic Approach

The control design problem for a class of constrained uncertain systems is considered in this paper. The uncertainty in the system, including unknown system parameters and external disturbance, is nonlinear and time-varying. The bound of the uncertainty is described via a fuzzy set. The states of the system are constrained to be bounded. A one-to-one state transformation is proposed to convert the bounded state constrained system into the unconstrained system. A new robust control scheme is then proposed for the transformed system, which is in deterministic form and not fuzzy if-then rule based. By fuzzy description of the uncertainty bound, the optimal design of the control gain is proposed, which minimizes a fuzzy performance index associated with both the fuzzy system performance and the control effort. The analytic solution to the optimization problem is demonstrated to always exist and be unique. The resulting control can guarantee uniform boundedness and uniform ultimate boundedness of the uncertain system, while minimizing the fuzzy-based performance index. In addition, the state constraint can be always guaranteed.