期刊
IET CONTROL THEORY AND APPLICATIONS
卷 14, 期 3, 页码 481-489出版社
INST ENGINEERING TECHNOLOGY-IET
DOI: 10.1049/iet-cta.2019.0270
关键词
stochastic processes; game theory; linear quadratic control; Riccati equations; stochastic games; stochastic systems; closed loop systems; linear-quadratic mean-field game; stochastic large-population systems; jump diffusion; mean-field game problem; Poisson processes; individuals; stochastic Hamiltonian system; Riccati equation; control problem; decentralised optimal strategies; open-loop; closed-loop form; limit representation; average term; practical control problems
资金
- National Natural Science Foundation of China [11801317, 11871310, 61573217, 11831010]
- Natural Science Foundation of Shandong Province [ZR2019MA013]
- Colleges and Universities Youth Innovation Technology Program of Shandong Province [2019KJI011]
- National High-level personnel of special support program of China
- Changjiang scholar program of Chinese Ministry of Education
This study is concerned with linear-quadratic mean-field game problem for a class of stochastic large-population systems with Poisson processes. The control is allowed to enter the jump diffusion terms of the individuals' state equation. By virtue of the stochastic Hamiltonian system and Riccati equation for limiting control problem, the decentralised optimal strategies are represented in the open-loop and closed-loop forms, respectively. Different from the existing results, the limit representation of average term is proposed in closed-loop form via the separation technique. Meanwhile, the decentralised optimal strategies are verified to be the epsilon-Nash equilibrium of the original problem. Finally, two practical control problems in engineering and economics areas are presented to demonstrate the good performance of theoretical results.
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