Controllability of Nash Equilibrium in Game-Based Control Systems

doi:10.1109/TAC.2019.2893150

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	Controllability of Nash Equilibrium in Game-Based Control Systems
	Zhang, Ren-Ren; Guo, Lei
	2019-10-01
发表期刊	IEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN	0018-9286
卷号	64 期号:10 页码:4180-4187
摘要	Controlling complex systems to desired states is of primary importance in science and engineering. In the classical control framework, the plants to be controlled usually do not have their own payoff or objective functions; however, this is not the case in many practical situations in, for examples, social, economic, and "intelligent" engineering systems. This motivates our introduction of the game-based control system (GBCS), which has a hierarchical decision-making structure: one regulator and multiple agents. The regulator is regarded as the global controller that makes decision first, and then, the agents try to optimize their respective objective functions to reach a possible Nash equilibrium as a result of noncooperative dynamic game. A fundamental issue in the GBCS is: Is it possible for the regulator to change the macrostates by regulating the Nash equilibrium formed by the agents at the lower level? This leads to the investigation of controllability of the Nash equilibrium of the GBCS. In this paper, we will first formulate this new problem in a general nonlinear framework and then focus on linear systems. Some explicit necessary and sufficient algebraic conditions on the controllability of the Nash equilibrium are given for a linear GBCS, by solving the controllability problem of the associated forward and backward dynamic equations, which is a key technical issue and has rarely been explored in the literature.
关键词	Controllability hierarchical structure maximum principle Nash equilibrium noncooperative differential games
DOI	10.1109/TAC.2019.2893150
语种	英语
资助项目	National Natural Science Foundation of China[11688101] ; National Natural Science Foundation of China[91634203] ; National Natural Science Foundation of China[61227902]
WOS研究方向	Automation & Control Systems ; Engineering
WOS类目	Automation & Control Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000490772500017
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35821
专题	国家数学与交叉科学中心
通讯作者	Guo, Lei
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Ren-Ren,Guo, Lei. Controllability of Nash Equilibrium in Game-Based Control Systems[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL,2019,64(10):4180-4187.
APA	Zhang, Ren-Ren,&Guo, Lei.(2019).Controllability of Nash Equilibrium in Game-Based Control Systems.IEEE TRANSACTIONS ON AUTOMATIC CONTROL,64(10),4180-4187.
MLA	Zhang, Ren-Ren,et al."Controllability of Nash Equilibrium in Game-Based Control Systems".IEEE TRANSACTIONS ON AUTOMATIC CONTROL 64.10(2019):4180-4187.