Near-Optimal Incentive Stackelberg Strategies for Singularly Perturbed Systems

Abstract

When the systems contain clow and fast modes. the Stackelberg games are numerical stiffness and ill-conditioning. It is necessary to find some methods to alleviate this ill-conditioning and to reduce the amount of computation. In this paper, we propose a method to treat linear-quadratic Stackelberg games for singularly perturbed systems. To obtain a series of well-conditioned and reduced-order problems, we assume, at first, that the follower responds to the leader’s incentive strategy with composite strategy. A near team-optimal incentive strategy, which contains the follower's composite strategy as information, is constructed by solving these reduced-order problems. And then we prove that the near-team-optimal incentive strategy is well-posed in the sense that the resulting value of the cost function for the leader will have the same limit with the full-order team value of the leader’s cost function as the small singular perturbation parameter e tends to zero, even if the follower responds to the leader’s incentive streategy with full-order strategy.