Optimal fuzzy adaptive control for uncertain flexible joint manipulator based on <i>D</i> ‐operation

Abstract

A fuzzy approach to the optimal control design for a kind of uncertain flexible joint manipulator is proposed. The system contains mismatched uncertainty which is described by fuzzy set theory and is assumed to be bounded. By implanting a fictitious control and transforming the system with new state variables, an adaptive robust controller is designed to guarantee the uniform boundedness and uniform ultimate boundedness of the transformed system. The proposed control is only based on the existence of the uncertainty bound and is not if–then heuristic rules‐based. Furthermore, the performance of the original system is also proven theoretically. By applying D ‐operation, the optimal design problem associated with the control can then be solved by minimising a constrained performance index. The performance index, which is based on the fuzzy information, includes average fuzzy system performance and control effort. The resulting control design is systematic and is able to assure the deterministic performance as well as the fuzzy performance. An illustrative example is given to demonstrate the authors' conclusions.