Optimal Control via Weighted Congestion Game with Linear Cost Functions
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- 英文论文题名：Optimal Control via Weighted Congestion Game with Linear Cost Functions
- 论文作者：Sisi Pan ; Yupeng Qiao
- 英文论文作者：Sisi Pan ; Yupeng Qiao ; Key Laboratory of Autonomous System and Network Control ; College of Automation Science and Engineering ; South China University of Technology
- 年：2017
- 作者机构：Key Laboratory of Autonomous System and Network Control,College of Automation Science and Engineering,South China University of Technology;
- 英文论文关键词：Optimal control ; Weighted congestion game ; Linear cost functions ; Profile dynamics ; Lyapunov-based approaches
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：O232
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：5
- 文件大小：205k
- 原文格式：D
- 会议级别：全国
摘要
This paper considers the optimal control via weighted congestion game with linear cost functions. First, the weighted congestion game is converted into a matrix form for the sake of simplicity of computation. Second, a system performance criteria is proposed in order to minimize individual cost, and by designing proper parameters of linear cost functions, the given system performance criterion is converted into weighted potential function of a weighted congestion game. Then the profile dynamics is expressed into an algebraic form and potential-based stability of weighted congestion game is considered by using the Lyapunov-based approaches. Finally, an example is given to illustrate the theoretical results.
This paper considers the optimal control via weighted congestion game with linear cost functions. First, the weighted congestion game is converted into a matrix form for the sake of simplicity of computation. Second, a system performance criteria is proposed in order to minimize individual cost, and by designing proper parameters of linear cost functions, the given system performance criterion is converted into weighted potential function of a weighted congestion game. Then the profile dynamics is expressed into an algebraic form and potential-based stability of weighted congestion game is considered by using the Lyapunov-based approaches. Finally, an example is given to illustrate the theoretical results.
This paper considers the optimal control via weighted congestion game with linear cost functions. First, the weighted congestion game is converted into a matrix form for the sake of simplicity of computation. Second, a system performance criteria is proposed in order to minimize individual cost, and by designing proper parameters of linear cost functions, the given system performance criterion is converted into weighted potential function of a weighted congestion game. Then the profile dynamics is expressed into an algebraic form and potential-based stability of weighted congestion game is considered by using the Lyapunov-based approaches. Finally, an example is given to illustrate the theoretical results.
引文
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[8]Y.Hao,S.Pan,Y.Qiao,D.Cheng,Cooperative control via congestion game approach,,IEEE Trans.Aut.Contr,Submitted,2016.
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[11]W.Feng,L.Wang,Q.Wang,A family of multi-path congestion control algorithms with global stability and delay robustness,Automatica,Vol.50,3112-3122,2014.
[12]H.Qi,Y.Wang,T.Liu,D.Cheng,Vector space structure of finite evolutionary games and its application to strategy profile convergence,J.Syst.Sci.Comples,Vol.29,602-628,2016.
[13]D.Cheng,H.Qi,Z.Li,Analysis and Control of Boolean Networks-A Semi-tensor Product Approach,Springer,London,2011.
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[2]X.Wang,N.Xiao,T.Wongpiromsarn,L.Xie,E.Frazzoli,D.Rus,Distributed consensus in noncooperative congestion games:an application to road pricing,Proc.10th IEEE Int.Conf.Contr.Aut.,Hangzhou,China,1668-1673,2013.
[3]T.Heikkinen,A potential game approach to distributed power control and scheduling,Computer Network,Vol.50,2295-2311,2005.
[4]R.W.Rosenthal,A class of games possessing pure-strategy Nash equilibria,Int.J.Game Theory,Vol.2,65-67,1973.
[5]J.R.Marden,G.Arslan,J.S.Shamma,Cooprative control and potential games,IEEE Trans.Sys.Man.Cyber.-Part B:Cyber.,Vol.39,No.6,1393-1407,2009.
[6]A.Y.Yazicioglu,M.Egerstedt,J.S.Shamma,A game theoretic approach to distributed coverage of graphs by heterogeneous mobile agents,Est.Contr.Netw.Sys.,Vol.4,309-315,2013.
[7]R.Gopalakrishnan,J.R.Marden,A.Wierman,An architectural view of game theoretic control,Performance Evaluation Review,Vol.38,No.3,31-36,2011.
[8]Y.Hao,S.Pan,Y.Qiao,D.Cheng,Cooperative control via congestion game approach,,IEEE Trans.Aut.Contr,Submitted,2016.
[9]D.Fotakis,S.Kontogiannis,P.Spirakis,Selfish unsplittable flows,Proceedings of the 31th International Colloquium on Automata,Languages and Programming(ICALP),593-605,2004.
[10]M.Mavronicolas,M.Milchtaich,I.Monien,B.Tiemann,K.Tiemann,Congestion games with player-specific constants,In:MFCS,2007.
[11]W.Feng,L.Wang,Q.Wang,A family of multi-path congestion control algorithms with global stability and delay robustness,Automatica,Vol.50,3112-3122,2014.
[12]H.Qi,Y.Wang,T.Liu,D.Cheng,Vector space structure of finite evolutionary games and its application to strategy profile convergence,J.Syst.Sci.Comples,Vol.29,602-628,2016.
[13]D.Cheng,H.Qi,Z.Li,Analysis and Control of Boolean Networks-A Semi-tensor Product Approach,Springer,London,2011.
[14]D.Cheng,H.Qi,Y.Zhao,An Introduction to Semi-tensor Product of Matrices and Its Applications,World Scientific,Singapore,2012.
[15]X.Zhang,Matrix Analysis and Applications,Tsinghua Univ.Press,Beijing,2004(in Chinese).
[16]D.Monderer,L.S.Shapley,Potential Games,Games and Economic Behavior,Vol.14,124-143,1996.
[17]H.P.Young,The evolution of conventions,Econometrica,Vol.61,57-84,1993.
[18]Y.Wang,D.Cheng,Stability of evolutionary games with time-varying payoffs,Proceedings of the 35th Chinese Control Conference,579-584,2016.