Optimal Design of Constraint-Following Control for Fuzzy Mechanical Systems

Abstract

The control problem for a mechanical system to follow a constraint is formulated. The uncertainty is considered in both the system dynamics and constraint. It is bounded, and the knowledge of the bound only lies within a fuzzy set. We propose an adaptive robust control for the mechanical system for approximate constraint-following. Both the mechanical system model and control scheme are deterministic and not if-then heuristic rules-based. An optimal design problem using the fuzzy description of the uncertainty is proposed. We prove that the global solution to the resulting optimization problem always exists and is unique. Under the control, the performance of the mechanical system is both deterministically guaranteed and fuzzily optimized.