Optimal actuator location of minimum norm controls for heat equation with general controlled domain

doi:10.1016/j.jde.2016.05.037

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	Optimal actuator location of minimum norm controls for heat equation with general controlled domain
	Guo, Bao-Zhu1,2,3 ; Xu, Yashan 4; Yang, Dong-Hui 5,6
刊名	JOURNAL OF DIFFERENTIAL EQUATIONS
	2016-09-15
卷号	261 期号:6 页码:3588-3614
关键词	Heat equation Optimal control Optimal location Game theory Nash equilibrium
ISSN号	0022-0396
DOI	10.1016/j.jde.2016.05.037
英文摘要	In this paper, we study optimal actuator location of the minimum norm controls for a multi-dimensional heat equation with control defined in the space L-2(Omega x (0, T)). The actuator domain is time-varying in the sense that it is only required to have a prescribed Lebesgue measure for any moment. We select an optimal actuator location so that the optimal control takes its minimal norm over all possible actuator domains. We build a framework of finding the Nash equilibrium so that we can develop a sufficient and necessary condition to characterize the optimal relaxed solutions for both actuator location and corresponding optimal control of the open -loop system. The existence and uniqueness of the optimal classical solutions are therefore concluded. As a result, we synthesize both optimal actuator location and corresponding optimal control into a time-varying feedbacks. (C) 2016 Elsevier Inc. All rights reserved.
资助项目	National Natural Science Foundation of China[11371375] ; National Natural Science Foundation of China[11471080] ; National Natural Science Foundation of China[11371095] ; China Postdoctoral Science Foundation ; Central South University Postdoctoral Science Foundation ; National Research Foundation of South Africa
WOS研究方向	Mathematics
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000381062700022
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/23463]
专题	系统科学研究所
通讯作者	Xu, Yashan
作者单位	1.Shanxi Univ, Sch Math, Taiyuan 030006, Peoples R China 2.Acad Sinica, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Univ Witwatersrand, Sch Comp Sci & Appl Math, ZA-2050 Johannesburg, South Africa 4.Fudan Univ, Sch Math Sci, KLMNS, Shanghai 200433, Peoples R China 5.Cent S Univ, Sch Math & Stat, Changsha 410075, Hunan, Peoples R China 6.Cent S Univ, Sch Informat Sci & Engn, Changsha 410075, Hunan, Peoples R China
推荐引用方式 GB/T 7714	Guo, Bao-Zhu,Xu, Yashan,Yang, Dong-Hui. Optimal actuator location of minimum norm controls for heat equation with general controlled domain[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2016,261(6):3588-3614.
APA	Guo, Bao-Zhu,Xu, Yashan,&Yang, Dong-Hui.(2016).Optimal actuator location of minimum norm controls for heat equation with general controlled domain.JOURNAL OF DIFFERENTIAL EQUATIONS,261(6),3588-3614.
MLA	Guo, Bao-Zhu,et al."Optimal actuator location of minimum norm controls for heat equation with general controlled domain".JOURNAL OF DIFFERENTIAL EQUATIONS 261.6(2016):3588-3614.