Closed-loop Stackelberg strategies for linear-quadratic descriptor systems

Abstract

In this paper, we investigate the linear-quadratic closed-loop Stackelberg game for the descriptor system. It is different from the Stackelberg game in the state-space system in that there may exist a descriptor variable feedback closed-loop incentive strategy in the Stackelberg game for the descriptor system. Sufficient conditions for the existence of such an incentive strategy are derived for both the finite-time and infinite-time cases. In addition, since there are two different decision makers in the Stackelberg games, it is not logical to assume that these different decision makers adopt the same reduced-order transformation to deal with their problems. We show that, if the system considered by the follower has index one, which can be guaranteed by the leader's incentive strategy, then the fact that the two decision makers adopt different reduced-order transformations does not affect the solution of the problem.