Cooperative Game Oriented Optimal Design in Controlling Uncertain Underactuated Mechanical Systems

Abstract

This paper examines the adaptive robust control for uncertain underactuated mechanical systems. The uncertainty is time varying but bounded. An adaptive robust constraint-following control approach is developed with tunable parameters. For the seeking of optimal control parameters, a two-player cooperative game oriented optimal design problem is formulated. The problem is completely solved with the existence and uniqueness of the optimal solution proved and the analytical expression of the optimal parameters provided. Using the optimal parameters, the proposed adaptive robust control renders dual performance: guaranteed (uniform boundedness and uniform ultimate boundedness) and optimal.