Optimal Design of Adaptive Robust Control for Bounded Constraint-Following Error in Fuzzy Mechanical Systems

Abstract

This paper proposes an optimal indirect approach for asymmetric bounds in constraint-following in mechanical systems with (possibly fast) time-varying fuzzy uncertainty. The uncertainty is described with fuzzy set theory. We aim at optimal controller to drive the constraint-following error of the concerned fuzzy system to lie within a desired (possibly asymmetric) bound all the time and get to be sufficiently small eventually. For deterministic performance, we transform the fuzzy original system into a constructed fuzzy system, for which a deterministic (not the usual if-then rules-based) adaptive robust control is designed for uniform boundedness and uniform ultimate boundedness. For optimal performance, a performance index is proposed based on the fuzzy information, by minimizing which an optimal control gain design problem is formulated and solved. When the constructed fuzzy system is uniform boundedness and uniform ultimate boundedness, the constraint-following error of the original fuzzy system is proved to be bounded. As a result, the control design can render out deterministic performance and minimum performance index.