A Stackelberg Game-Theoretic Exploration Rendering Robustness and Optimality for Performance Improvement of Fuzzy Mechanical Systems

We consider mechanical systems with uncertainty. The uncertainty may be time varying. The bound of the uncertainty is described by its fuzzy characteristics. To design a feasible control, we start with a robust phase, which renders a control scheme that guarantees the system performance regardless of the actual value of the uncertainty. This robust phase is then followed by an optimal phase. There are design parameters in the control, which can be fine-tuned. We proposed multiple performance objectives. The goal of the choice of the control design parameters is to minimize the performance objectives. However, since these objectives are nonconciliating (meaning one’s minimum is not the other one’s minimum), we invoke the Stackelberg strategy for the optimal parameters. The game strategy mimics two players: one is the leader and one is the follower. Through the interplay between the two players, we show how to select the design parameters. The design procedure in both robust and optimal phases is demonstrated by a coupled inverted pendulum system.