1. Incentive Stackelberg game for H∞$H_\infty$‐constrained multi‐hierarchy systems under observation information.
- Author
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Li, Xiaoqian, Bai, Mengyu, Zhang, Huanshui, Jing, Zonglei, Ju, Peijun, and Guo, Zhongjin
- Subjects
INCENTIVE (Psychology) ,RICCATI equation ,NASH equilibrium ,GAMES - Abstract
This paper considers the incentive feedback Stackelberg game with multi‐hierarchy players under a H∞$H_\infty$ constraint, with the proposed solution involving nested hierarchies A and B. In hierarchy A, P0 represents the leader (the leader's control input corresponding to i‐th follower, i=1,2,...,n$i=1,2,\ldots ,n$), and P1,...,Pn$P_1,\ldots ,P_n$ are the followers, with non‐cooperative followers induced to virtually cooperate in achieving team‐optimal solution and the Nash equilibrium. In hierarchy B, the external disturbance represents the follower, and hierarchy A represents the leader. The main contributions of this work are three‐fold. First, an incentive Stackelberg strategy set under the H∞$H_\infty$ constraint through observation information is obtained for the first time. Second, a novel iterative algorithm to solve the coupled backward and forward Riccati equations is introduced and thus obtaining an explicit expression of a team‐optimal feedback Stackelberg strategy set with an H∞$H_\infty$ constraint. Finally, the necessary and sufficient conditions for the existence and uniqueness of the hierarchical game's optimal solutions using the Lyapunov equation and the induction algorithm are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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