Nash Equilibrium Precision Controllability and Linear Quadratic Optimal Control for Stochastic Switched Systems
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- 英文论文题名：Nash Equilibrium Precision Controllability and Linear Quadratic Optimal Control for Stochastic Switched Systems
- 论文作者：Zhang ting rui ; Liu Feng
- 英文论文作者：Zhang ting rui ; Liu Feng ; Center for Intelligent Systems and Renewable Energy ; School of Electronics and Information Engineering ; Beijing Jiaotong University
- 年：2017
- 作者机构：Center for Intelligent Systems and Renewable Energy,School of Electronics and Information Engineering,Beijing Jiaotong University;
- 英文论文关键词：non-cooperative dynamic game ; Nash equilibrium ; stochastic switched systems ; forwardCbackward stochastic differential equation(FBSDE) ; exact controllability
- 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：187k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, a class of stochastic switched systems based on non-cooperative dynamic games has been considered,and the dynamic game involves one leader and multiple followers. From the viewpoint of the forward and backward stochastic differential equations(FBSDE), a sufficient and necessary condition characterizing the Nash Equilibrium stochastic exact controllability and algebraic criteria of the system are obtained, it is interesting that If the stochastic system degenerate to deterministic systems,the condition for stochastic exact controllability becomes the counterpart for complete controllability of linear deterministic control systems.
In this paper, a class of stochastic switched systems based on non-cooperative dynamic games has been considered,and the dynamic game involves one leader and multiple followers. From the viewpoint of the forward and backward stochastic differential equations(FBSDE), a sufficient and necessary condition characterizing the Nash Equilibrium stochastic exact controllability and algebraic criteria of the system are obtained, it is interesting that If the stochastic system degenerate to deterministic systems,the condition for stochastic exact controllability becomes the counterpart for complete controllability of linear deterministic control systems.
In this paper, a class of stochastic switched systems based on non-cooperative dynamic games has been considered,and the dynamic game involves one leader and multiple followers. From the viewpoint of the forward and backward stochastic differential equations(FBSDE), a sufficient and necessary condition characterizing the Nash Equilibrium stochastic exact controllability and algebraic criteria of the system are obtained, it is interesting that If the stochastic system degenerate to deterministic systems,the condition for stochastic exact controllability becomes the counterpart for complete controllability of linear deterministic control systems.
引文
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[7]Chai Meiqun,Liu Aiying.Research on Information Symmetry Theory Framework Innovation[J].Journal of Business Economics,2014(1):8-10.
[8]Zhu H,Zhang C.Infinite time horizon nonzero-sum linear quadratic stochastic differential games with state and controldependent noise[J].Control Theory and Technology,2013,11(4):629-633.
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[10]Feng L,Song Y D.Stability condition for sampled data based control of linear continuous switched systems[J].Systems and Control Letters,2011,60(10):787-797.
[11]F.Liu,S.G.Peng,On Controllability for Stochastic Control Systems When the Coefficient is Time-variant[J].Journal of Systems Science and Complexity.2010,23:270-278.
[12]Yong J,Zhou X Y.Stochastic controls:Hamiltonian systems and HJB equations[J].Automatic Control IEEE Transactions on,2012,46(11):1846-1846.
[13]Yong J.Forward-backward stochastic differential equations with mixed initial-terminal conditions[J].Transactions of the American Mathematical Society,2010,362(2):1047-1096.
[14]S.Peng,Backward stochastic differential equation and exact controllability of stochastic control systems[J].Progress in Natural Science,1994,4(3),274-284.
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[2]He Xiao qun,Game theory and modern market economy[J].China Academic Journal Network Publishing Database,1995,04(10)33-35.
[3]Wan B W.The global economic crisis and lessons drawn in the viewpoint of economic cybernetics(analogy study and review)-To commemorate the 120 anniversary of the birth of the founder of Cybernetics Norbert Wiener(1894-2014)[J].Control Theory and Applications,2014.
[4]Huang G S,Zhou J M,Zhong S W,Zhao W,Game model for rational expectation of national income[J].Control Theory and Application,2003,20(4):529-532.
[5]Zhang Weiying,Game theory and information economics[M].Shanghai People’s Publishing House,1996.
[6]Stiglitz,Joseph E.The Journal of Economic Perspectives and the Marketplace of Ideas:A View from the Founding[J].Journal of Economic Perspectives.Spring,2012,vol.26 Issue 2,p19-26.8p.
[7]Chai Meiqun,Liu Aiying.Research on Information Symmetry Theory Framework Innovation[J].Journal of Business Economics,2014(1):8-10.
[8]Zhu H,Zhang C.Infinite time horizon nonzero-sum linear quadratic stochastic differential games with state and controldependent noise[J].Control Theory and Technology,2013,11(4):629-633.
[9]Engwerda J C.On the Open-loop Nash Equilibrium in LQgames[J].Journal of Economic Dynamics and Control,1998,22(5):729-762.
[10]Feng L,Song Y D.Stability condition for sampled data based control of linear continuous switched systems[J].Systems and Control Letters,2011,60(10):787-797.
[11]F.Liu,S.G.Peng,On Controllability for Stochastic Control Systems When the Coefficient is Time-variant[J].Journal of Systems Science and Complexity.2010,23:270-278.
[12]Yong J,Zhou X Y.Stochastic controls:Hamiltonian systems and HJB equations[J].Automatic Control IEEE Transactions on,2012,46(11):1846-1846.
[13]Yong J.Forward-backward stochastic differential equations with mixed initial-terminal conditions[J].Transactions of the American Mathematical Society,2010,362(2):1047-1096.
[14]S.Peng,Backward stochastic differential equation and exact controllability of stochastic control systems[J].Progress in Natural Science,1994,4(3),274-284.
[15]E.Pardoux,S.Peng,Adaptive solution of a backward stochastic differential equation[J],Systems and Control Letters,1990,14(1),55-61.