Mean Field Games for Multiagent Systems with Control-dependent Multiplicative Noises
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- 英文论文题名：Mean Field Games for Multiagent Systems with Control-dependent Multiplicative Noises
- 论文作者：Bing-Chang Wang ; Yuan-Hua Ni ; Dan-Dan Pang
- 英文论文作者：Bing-Chang Wang ; Yuan-Hua Ni ; Dan-Dan Pang ; Bingchang Wang is with School of Control Science and Engineering ; Shandong University ; College of Computer and Control Engineering ; Nankai University ; School of Information and Electrical Engineering ; Shandong Jianzhu University
- 年：2017
- 作者机构：Bingchang Wang is with School of Control Science and Engineering,Shandong University;College of Computer and Control Engineering,Nankai University;School of Information and Electrical Engineering,Shandong Jianzhu University;
- 英文论文关键词：mean field game ; multiplicative noise ; decentralized strategy ; asymptotic average consensus
- 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：O225
- 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：6
- 文件大小：262k
- 原文格式：D
- 会议级别：全国
摘要
This paper studies mean field games for multiagent systems with multiplicative noises. By solving an auxiliary limiting optimal control problems subject to consistent mean field approximations, a set of decentralized strategies is obtained and further shown to be an asymptotical Nash equilibrium. Then, we apply the result to the consensus problem for the model of single integrators with multiplicative noises. It is shown that under the proposed strategies all the agents achieve asymptotic average consensus in the mean square sense.
This paper studies mean field games for multiagent systems with multiplicative noises. By solving an auxiliary limiting optimal control problems subject to consistent mean field approximations, a set of decentralized strategies is obtained and further shown to be an asymptotical Nash equilibrium. Then, we apply the result to the consensus problem for the model of single integrators with multiplicative noises. It is shown that under the proposed strategies all the agents achieve asymptotic average consensus in the mean square sense.
This paper studies mean field games for multiagent systems with multiplicative noises. By solving an auxiliary limiting optimal control problems subject to consistent mean field approximations, a set of decentralized strategies is obtained and further shown to be an asymptotical Nash equilibrium. Then, we apply the result to the consensus problem for the model of single integrators with multiplicative noises. It is shown that under the proposed strategies all the agents achieve asymptotic average consensus in the mean square sense.
引文
[1]M.Ait Rami,and X.Y.Zhou.Linear matrix inequalities,Riccati equations,and indefinite stochastic linear quadratic control.IEEE Transactions on Automatic Control,45,1131 1142,2000.
[2]A.Bensoussan,J.Frehse,and P.Yam.Mean Field Games and Mean Field Type Control Theory.Springer,New York,2013.
[3]R.Carmona and F.Delarue.Probabilistic analysis of meanfield games.SIAM J.Control Optim.,vol.51,no.4,pp.2705-2734,2013.
[4]K.Chung,A Course in Probability Theory,2nd Edition,Academic Press,2000.
[5]D.A.Gomes and J.Saude.Mean field games models–a brief survey.Dyn.Games Appl.,vol.4,no.2,pp.110-154,2014.
[6]M.Huang,Large-population LQG games involving a major player:the Nash certainty equivalence principle,SIAM J.Control and Optim.,vol.48,no.5,pp.3318–3353,2010.
[7]M.Huang,P.E.Caines,and R.P.Malhamé,Individual and mass behaviour in large population stochastic wireless power control problems:Centralized and Nash equilibrium solutions.Proc.42nd IEEE CDC,Maui,HI,pp.98-103,Dec.2003.
[8]M.Huang,P.E.Caines and R.P.Malhamé,Largepopulation cost-coupled LQG problems with non-uniform agents:Individual-mass behavior and decentralized-Nash equilibria.IEEE Trans.Autom.Control,vol.52,pp.1560-1571,2007.
[9]M.Huang,R.P.Malhamé,and P.E.Caines,Large population stochastic dynamic games:Closed-loop Mc Kean-Vlasov systems and the Nash certainty equivalence principle.Commun.Inform.Syst.,vol.6,pp.221-251,2006.
[10]M.Huang and J.H.Manton.Coordination and consensus of networked agents with noisy measurements:stochastic algorithms and asymptotic behavior.SIAM J.Control and Optim.,vol.48,no.1,pp.134-161,2009.
[11]J.M.Lasry and P.L.Lions,Mean field games.Japan J.Math.,vol.2,pp.229-260,2007.
[12]T.Li and J.-F.Zhang,Asymptotically optimal decentralized control for large population stochastic multiagent systems.IEEE Trans.Autom.Control,vol.53,no.7,pp.1643-1660,2008.
[13]T.Li and J.-F.Zhang,Mean square average consensus under measurement noises and fixed topologies:necessary and sufficient conditions,Automatica,vol.45,No.8,1929-1936,2009.
[14]T.Li,F.K.Wu and J.-F.Zhang,Multi-agent consensus with relative-state-dependent measurement noises,IEEE Trans.on Automatic Control,vol.59,No.9,2463-2468,2014.
[15]Z.Li,M.Fu,H.Zhang and Z.Wu.Mean field stochastic linear quadratic games for continuum-parameterized multiagent systems,preprint,2017.
[16]Y.-H.Ni,and X.Li,Consensus seeking in multi-agent systems with multiplicative measurement noises.Systems&Control Letters,62(5),430 437,2013.
[17]Y.H.Ni,J.F.Zhang,and X.Li,Indefinite Mean-Field Stochastic Linear-Quadratic Optimal Control.IEEE Trans.Automat.Contr.,vol.60,no.7,pp.1786-1800,2015.
[18]M.Nourian,P.E.Caines,R.P.Malhame,M.Y.Huang,Nash,Social and centralized solutions to consensus problems via mean field control theory.IEEE Trans.on Automatic Control.vol.58,no.3,2013,pp.639-653.
[19]M.Nourian,P.E.Caines,R.P.Malhame,A mean field game synthesis of initial mean consensus problems:A continuum approach for Non-Gaussian Behaviour.IEEE Trans.on Automatic Control,vol.59,no.2,2014,pp.449-455.
[20]H.Tembine,Q.Zhu,and T.Basar.Risk-sensitive mean-field games.IEEE Trans.Autom.Control,vol.59,no.4,pp.835-850,2014.
[21]B.-C.Wang and J.-F.Zhang.Consensus conditions of multiagent systems with unbalanced topology and stochastic disturbances,Journal of Systems Science and Mathematical Sciences,vol.29,no.10,1353-1365,2009.
[22]B.-C.Wang and J.-F.Zhang.Distributed control of multiagent systems with random parameters and a major agent,Automatica,Vol.48,No.9,2093-2106,2012.
[23]B.-C.Wang and J.-F.Zhang.Mean field games for largepopulation multiagent systems with Markov jump parameters.SIAM J.Control Optim,vol.50,no.4,pp.2308-2334,2012.
[24]B.-C.Wang and J.-F.Zhang.Hierarchical mean field games for multiagent systems with tracking-type costs:Distributed-Stackelberg equilibria.IEEE Trans.Autom.Control,Vol.59,No.8,pp.2241-2247,2014.
[25]G.Weintraub,C.Benkard,and B.Van Roy,Markov perfect industry dynamics with many firms,Econometrica,vol.76,no.6,pp.1375–1411,2008.
[26]J.Yong and X.Zhou.Stochastic controls:Hamiltonian systems and HJB equations.Springer,Newyork,1999.
[27]H.Zhang and J.Xu,Control for Ito Stochastic Systems With Input Delay.IEEE Trans.Autom.Control,vol.62,no.1,pp.350-365,2017.
[2]A.Bensoussan,J.Frehse,and P.Yam.Mean Field Games and Mean Field Type Control Theory.Springer,New York,2013.
[3]R.Carmona and F.Delarue.Probabilistic analysis of meanfield games.SIAM J.Control Optim.,vol.51,no.4,pp.2705-2734,2013.
[4]K.Chung,A Course in Probability Theory,2nd Edition,Academic Press,2000.
[5]D.A.Gomes and J.Saude.Mean field games models–a brief survey.Dyn.Games Appl.,vol.4,no.2,pp.110-154,2014.
[6]M.Huang,Large-population LQG games involving a major player:the Nash certainty equivalence principle,SIAM J.Control and Optim.,vol.48,no.5,pp.3318–3353,2010.
[7]M.Huang,P.E.Caines,and R.P.Malhamé,Individual and mass behaviour in large population stochastic wireless power control problems:Centralized and Nash equilibrium solutions.Proc.42nd IEEE CDC,Maui,HI,pp.98-103,Dec.2003.
[8]M.Huang,P.E.Caines and R.P.Malhamé,Largepopulation cost-coupled LQG problems with non-uniform agents:Individual-mass behavior and decentralized-Nash equilibria.IEEE Trans.Autom.Control,vol.52,pp.1560-1571,2007.
[9]M.Huang,R.P.Malhamé,and P.E.Caines,Large population stochastic dynamic games:Closed-loop Mc Kean-Vlasov systems and the Nash certainty equivalence principle.Commun.Inform.Syst.,vol.6,pp.221-251,2006.
[10]M.Huang and J.H.Manton.Coordination and consensus of networked agents with noisy measurements:stochastic algorithms and asymptotic behavior.SIAM J.Control and Optim.,vol.48,no.1,pp.134-161,2009.
[11]J.M.Lasry and P.L.Lions,Mean field games.Japan J.Math.,vol.2,pp.229-260,2007.
[12]T.Li and J.-F.Zhang,Asymptotically optimal decentralized control for large population stochastic multiagent systems.IEEE Trans.Autom.Control,vol.53,no.7,pp.1643-1660,2008.
[13]T.Li and J.-F.Zhang,Mean square average consensus under measurement noises and fixed topologies:necessary and sufficient conditions,Automatica,vol.45,No.8,1929-1936,2009.
[14]T.Li,F.K.Wu and J.-F.Zhang,Multi-agent consensus with relative-state-dependent measurement noises,IEEE Trans.on Automatic Control,vol.59,No.9,2463-2468,2014.
[15]Z.Li,M.Fu,H.Zhang and Z.Wu.Mean field stochastic linear quadratic games for continuum-parameterized multiagent systems,preprint,2017.
[16]Y.-H.Ni,and X.Li,Consensus seeking in multi-agent systems with multiplicative measurement noises.Systems&Control Letters,62(5),430 437,2013.
[17]Y.H.Ni,J.F.Zhang,and X.Li,Indefinite Mean-Field Stochastic Linear-Quadratic Optimal Control.IEEE Trans.Automat.Contr.,vol.60,no.7,pp.1786-1800,2015.
[18]M.Nourian,P.E.Caines,R.P.Malhame,M.Y.Huang,Nash,Social and centralized solutions to consensus problems via mean field control theory.IEEE Trans.on Automatic Control.vol.58,no.3,2013,pp.639-653.
[19]M.Nourian,P.E.Caines,R.P.Malhame,A mean field game synthesis of initial mean consensus problems:A continuum approach for Non-Gaussian Behaviour.IEEE Trans.on Automatic Control,vol.59,no.2,2014,pp.449-455.
[20]H.Tembine,Q.Zhu,and T.Basar.Risk-sensitive mean-field games.IEEE Trans.Autom.Control,vol.59,no.4,pp.835-850,2014.
[21]B.-C.Wang and J.-F.Zhang.Consensus conditions of multiagent systems with unbalanced topology and stochastic disturbances,Journal of Systems Science and Mathematical Sciences,vol.29,no.10,1353-1365,2009.
[22]B.-C.Wang and J.-F.Zhang.Distributed control of multiagent systems with random parameters and a major agent,Automatica,Vol.48,No.9,2093-2106,2012.
[23]B.-C.Wang and J.-F.Zhang.Mean field games for largepopulation multiagent systems with Markov jump parameters.SIAM J.Control Optim,vol.50,no.4,pp.2308-2334,2012.
[24]B.-C.Wang and J.-F.Zhang.Hierarchical mean field games for multiagent systems with tracking-type costs:Distributed-Stackelberg equilibria.IEEE Trans.Autom.Control,Vol.59,No.8,pp.2241-2247,2014.
[25]G.Weintraub,C.Benkard,and B.Van Roy,Markov perfect industry dynamics with many firms,Econometrica,vol.76,no.6,pp.1375–1411,2008.
[26]J.Yong and X.Zhou.Stochastic controls:Hamiltonian systems and HJB equations.Springer,Newyork,1999.
[27]H.Zhang and J.Xu,Control for Ito Stochastic Systems With Input Delay.IEEE Trans.Autom.Control,vol.62,no.1,pp.350-365,2017.