Optimal parameter selection for constraint-following control for mechanical systems based on Stackelberg game

Abstract

This paper proposes an optimal parameter design of control scheme for mechanical systems by adopting the Stackelberg game theory. The goal of the control is to drive the mechanical system to follow the prescribed constraints. The system uncertainty is (possibly fast) time-varying and bounded. A \(\beta \)-measure is defined to gauge the performance. A robust control is proposed to render the \(\beta \)-measure uniformly ultimately bounded. This control scheme is based on feasible design parameters (i.e., parameters within prescribed range), and the choices of these parameters may not be unique. For optimal (unique) parameter selection, a Stackelberg game is formulated. By taking the control design parameters as the players, for each player, a cost function is built with the consideration of the performance cost, the time cost and the control cost. To follow, the Stackelberg strategy is then carried out via backward induction, which results in the choice of the optimal parameters.