Incentive game approach to $H_{\infty}$ -constrained system with hierarchy decision makers
Zonglei Jing, Xiaoqian Li, Peijun Ju, Jianzhong Zhang · 2022 41st Chinese Control Conference (CCC) · 2022
In this paper, incentive game approach is introduced to deal with$H_{\infty}$-constrained system. In hierarchy A, the leader derives the leader's team-optimal solution while the non-cooperative followers are induced to get the Nash equilibrium. In hierarchy B, the hierarchy A plays the leader's role while the deterministic external disturbance is the follower. It is the first attempt to formulate the optimal filtering to$H_{\infty}$constraint feedback Stackelberg games with hierarchical decision players. By applying matrix maximum principle in hierarchy A and hierarchy B, respectively, solutions to forward and backward equations are presented. Conditions are given to guarantee the existence and the uniqueness of the optimal solutions by using Lyapunov equation.