LQG Differential Stackelberg Game Under Nested Observation Information Patterns

• 成果类型: Article
• 署名作者: Li, Zhipeng; Marelli, Damian; Fu, Minyue; Zhang, Huanshui
• 署名单位: University of Newcastle; Shandong University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3217268
• 发表日期: 2023
• 页码: 5111-5118
• 关键词: Index Terms-Backward stochastic differential equations (BS-DEs); differential Stackelberg game; Kalman filter; linear quadratic Gaussian (LQG) optimal control; separation principle

摘要

We investigate the linear quadratic Gaussian-Stackelberg game under a class of nested observation information patterns. The follower uses its observation data to design its strategy, whereas the leader implements its strategy using global observation data. We show that the solution requires solving a new type of forward-backward stochastic differential equation, whose drift components contain two conditional expectation terms associated with the adjoint variables. We then propose a method to find the functional relations between each adjoint pair, i.e., each pair formed by an adjoint variable and the conditional expectation of its associated state. The proposed method follows a layered pattern. More precisely, in the inner layer, we seek the functional relation for the adjoint pair under the sigma-subalgebra generated by follower's observation information, and in the outer layer, we look for the functional relation for the adjoint pair under the sigma-subalgebra generated by leader's observation information. Our result shows that the optimal open-loop solution admits an explicit feedback type representation.