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Hierarchical optimal control for input-affine nonlinear systems through the formulation of Stackelberg game
Mu, Chaoxu1; Wang, Ke1; Zhang, Qichao2,3; Zhao, Dongbin2,3
Source PublicationINFORMATION SCIENCES
ISSN0020-0255
2020-05-01
Volume517Pages:1-17
Corresponding AuthorMu, Chaoxu(cxmu@tju.edu.cn)
AbstractSubstantial efforts have been undertaken to explore nonzero-sum differential games. Most of these studies are devoted to devising algorithms to pursue Nash equilibrium, where all players with the same access to information will take policies synchronously. However, when it comes to hierarchical optimization and asymmetric information, Nash equilibrium is ineffective. The Stackelberg game provides us with an idea of leader-follower strategy to cope with this conundrum. The paper investigates hierarchical optimal control for continuous-time two-player input-affine systems characterized by nonlinear dynamics and quadratic cost functions. By introducing new costates, this optimization problem is formulated as a Stackelberg game in conjunction with a parametric optimization problem. Besides, the closed-loop information is available for both players. An adaptive learning algorithm is thus developed to approximately obtain the open-loop Stackelberg equilibrium while ensuring the uniform ultimate bounded stability of this closed-loop system, and two approximators structured by neural networks put this purpose into practice. Finally, two numerical examples illustrate that the proposed methodology can accurately obtain optimal solutions, and a comparative example illustrates its characteristics. (C) 2020 Elsevier Inc. All rights reserved.
KeywordNonzero-sum differential game Hierarchical optimization Nonlinear dynamics Stackelberg equilibrium Neural network
DOI10.1016/j.ins.2019.12.078
WOS KeywordSTRATEGIES ; ALGORITHM
Indexed BySCI
Language英语
Funding ProjectNational Natural Science Foundation of China[61773284] ; National Natural Science Foundation of China[61803371] ; National Natural Science Foundation of China[61533017] ; National Natural Science Foundation of China[61773284] ; National Natural Science Foundation of China[61803371] ; National Natural Science Foundation of China[61533017]
Funding OrganizationNational Natural Science Foundation of China
WOS Research AreaComputer Science
WOS SubjectComputer Science, Information Systems
WOS IDWOS:000517659200001
PublisherELSEVIER SCIENCE INC
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Document Type期刊论文
Identifierhttp://ir.ia.ac.cn/handle/173211/38383
Collection中国科学院自动化研究所
Corresponding AuthorMu, Chaoxu
Affiliation1.Tianjin Univ, Sch Elect & Informat Engn, Tianjin 300072, Peoples R China
2.Chinese Acad Sci, Inst Automat, State Key Lab Management & Control Complex Syst, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Mu, Chaoxu,Wang, Ke,Zhang, Qichao,et al. Hierarchical optimal control for input-affine nonlinear systems through the formulation of Stackelberg game[J]. INFORMATION SCIENCES,2020,517:1-17.
APA Mu, Chaoxu,Wang, Ke,Zhang, Qichao,&Zhao, Dongbin.(2020).Hierarchical optimal control for input-affine nonlinear systems through the formulation of Stackelberg game.INFORMATION SCIENCES,517,1-17.
MLA Mu, Chaoxu,et al."Hierarchical optimal control for input-affine nonlinear systems through the formulation of Stackelberg game".INFORMATION SCIENCES 517(2020):1-17.
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