CONTROLLABILITY OF STOCHASTIC GAME-BASED CONTROL SYSTEMS

doi:10.1137/18M120854X

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	CONTROLLABILITY OF STOCHASTIC GAME-BASED CONTROL SYSTEMS
	Zhang, Renren; Guo, Lei
	2019
发表期刊	SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN	0363-0129
卷号	57 期号:6 页码:3799-3826
摘要	It is well known that in classical control theory, the controller has a certain objective to achieve, and the plant to be controlled does not have its own objective. However, this is not the case in many practical situations in, for example, social, economic, and rapidly developing "intelligent" engineering systems. For these kinds of systems, the classical control theory cannot be applied directly. This motivates us to introduce a new control framework called game-based control systems (GBCSs), which has a hierarchical decision-making structure, i.e., a higher level regulator and lower level multiple agents. The regulator is regarded as the macrocontroller that makes decisions first, and then the agents try to optimize their respective objective functions, where a possible Nash equilibrium may be reached as a result of a noncooperative differential game. A fundamental issue in GBCSs is whether it is possible for the regulator to change the macrostates of the system by regulating the Nash equilibrium formed by the agents at the lower level. The investigation of this problem was initiated recently by the authors for deterministic systems. In this paper, we formulate this problem in the general stochastic nonlinear framework, and then focus on linear stochastic systems to give some explicit necessary and sufficient algebraic conditions on the controllability of the Nash equilibrium. In contrast to the classical controllability theory on forward differential equations, we now need to investigate the controllability of the associated forward-backward stochastic differential equations, which involves a more complicated investigation. Moreover, in the current stochastic case, which is more complicated than the deterministic case, we need some deep understanding of forward-backward stochastic differential equations.
关键词	noncooperative stochastic differential games hierarchical structure game-based control systems Nash equilibrium controllability forward-backward stochastic differential equations
DOI	10.1137/18M120854X
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[91634203] ; National Natural Science Foundation of China[11688101] ; National Natural Science Foundation of China[61227902]
WOS研究方向	Automation & Control Systems ; Mathematics
WOS类目	Automation & Control Systems ; Mathematics, Applied
WOS记录号	WOS:000544276200008
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51712
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Renren
作者单位	Chinese Acad Sci, AMSS, Inst Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Renren,Guo, Lei. CONTROLLABILITY OF STOCHASTIC GAME-BASED CONTROL SYSTEMS[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION,2019,57(6):3799-3826.
APA	Zhang, Renren,&Guo, Lei.(2019).CONTROLLABILITY OF STOCHASTIC GAME-BASED CONTROL SYSTEMS.SIAM JOURNAL ON CONTROL AND OPTIMIZATION,57(6),3799-3826.
MLA	Zhang, Renren,et al."CONTROLLABILITY OF STOCHASTIC GAME-BASED CONTROL SYSTEMS".SIAM JOURNAL ON CONTROL AND OPTIMIZATION 57.6(2019):3799-3826.