Optimizing constraint obedience for mechanical systems: Robust control and non-cooperative game

Abstract

This paper focuses on the optimization of constraint obedience for mechanical systems based on robust control design and non-cooperative game theory. The (possibly fast) time-varying but bounded system uncertainty is considered. First, it aims at a controller to drive the concerned system to follow a set of prescribed constraints. A problem of constraint-following is formulated with a β-measure as the gauge of constraint-following error, and then a robust control with two tunable parameters is proposed to render the measure to be uniformly bounded and uniformly ultimately bounded. Second, it aims at the optimal design of control parameters. A two-player non-cooperative game is formulated with two cost functions, each of which is dominated by one tunable parameter and consists of three parts: the state cost, the time cost and the control cost. Finally, the Nash equilibrium (i.e., the optimal control parameters) is obtained by minimizing the cost functions. By this, the optimization of constraint obedience for mechanical systems is achieved with the existence, uniqueness, and analytical expression of the Nash equilibrium.