Adaptive Robust Control for Fuzzy Mechanical Systems: Constraint-Following and Redundancy in Constraints

Motion control for uncertain mechanical systems is considered. Emphasis is on constraint following, while the constraint may be redundant. The uncertainty in the system, which is (possibly) fast time varying, is bounded. The bound is unknown but is assumed to be within a prescribed fuzzy set. An adaptive robust control is proposed based on the fuzzy property of the uncertainty. Both the mechanical system and the control are deterministic and, hence, not if-then fuzzy rule based. The performance of the resulting controlled system is twofold. First, some deterministic performance is guaranteed, regardless of the value of the uncertainty. Second, the minimization of a fuzzy-based performance index is guaranteed based on an optimal choice of a control design parameter. The effectiveness of the design procedure is illustrated by the simulation control of a digging excavator.