Possibility-Based Robust Control for Fuzzy Mechanical Systems

This study proposes a new robust control design framework for uncertain mechanical systems, which may be fullyactuated or underactuated. The uncertainty is (possibly fast) time-varying, lies in prescribed fuzzy sets (hence fuzzy mechanical systems), and may be unbounded. The control goal is formulated as servo constraints (hence constraint-following control), which may be holonomic or nonholonomic. We introduce the possibility theory into the Lyapunov stability analysis (LSA), proposing possibilitybased Lyapunov stability analysis (PBLSA), which allows a maximum failure possibility (generally small) prescribed by designers. It can be viewed as a generalization of the conventional LSA, and the resultant performance is interpreted in the context of possibility. By the PBLSA, a class of robust constraint-following controls that is not IF-THEN heuristic rules-based is proposed, which renders approximate constraint-following for the system performance with a prescribed maximal failure possibility. Optimal design of a control parameter considering both system performance and control cost is investigated. The benefits of the proposed design framework are discussed and simulations on two applications are given for demonstrations.