Robust Control Design with Optimization for Uncertain Mechanical Systems: Fuzzy Set Theory and Cooperative Game Theory

The merger between fuzzy set theory and cooperative game theory for dual control parameters optimization in robust control design of the uncertain mechanical system is investigated. The uncertainties in the mechanical system are assumed to be time-varying and bounded, though the value of bound is unknown, lie in the prescribed set expressed by the fuzzy set theory. A deterministic robust control approach is proposed to guarantee the primary performance (uniform boundedness and uniform ultimate boundedness) for the fuzzy mechanical system. There are two tunable control design parameters which relate to system performance and control cost. By utilizing the fuzzy set theory to describe uncertainty bound, a two-player cooperative game approach is introduced to formulate the optimal parameter design problem with two cost functions. The dual objective optimization problem is solved by seeking the Pareto-optimality for two players (i.e., the two parameters), whose solution is proved to exist in analytic form. Simulation results on the lower limb rehabilitation exoskeleton robot demonstrate the effectiveness of the proposed control scheme and optimization method.