Analytic solution to Indefinite Linear Quadratic Regulator for Stochastic Systems
详细信息 查看官网全文
- 英文论文题名：Analytic solution to Indefinite Linear Quadratic Regulator for Stochastic Systems
- 论文作者：Hongxia Wang ; Yunbo Zhao
- 英文论文作者：Hongxia Wang ; Yunbo Zhao ; Zhejiang University of Technology
- 年：2017
- 作者机构：Zhejiang University of Technology;
- 英文论文关键词：linear quadratic regulator ; stochastic systems ; forward backword stochastic differential equations ; Riccati equation
- 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：O231
- 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：195k
- 原文格式：D
- 会议级别：全国
摘要
This paper aims to deal with the indefinite linear quadratic regulator(ILQR) for stochastic systems. It provides both the analytic solution to the ILQR and the sufficient and necessary condition under which the ILQR is solvable. Different from the existed literature, we obtain the results in a novel way. In order to obtain a tighter necessary condition, we investigate the solution structure of a two-point boundary value problem for a stochastic differential equations directly but involve no complicated probabilistic derivation. Consider that there are close relationships between the linear game problem and H+∞ control and ILQR,the idea in the paper can also be extended to solve these problems.
This paper aims to deal with the indefinite linear quadratic regulator(ILQR) for stochastic systems. It provides both the analytic solution to the ILQR and the sufficient and necessary condition under which the ILQR is solvable. Different from the existed literature, we obtain the results in a novel way. In order to obtain a tighter necessary condition, we investigate the solution structure of a two-point boundary value problem for a stochastic differential equations directly but involve no complicated probabilistic derivation. Consider that there are close relationships between the linear game problem and H+∞ control and ILQR,the idea in the paper can also be extended to solve these problems.
This paper aims to deal with the indefinite linear quadratic regulator(ILQR) for stochastic systems. It provides both the analytic solution to the ILQR and the sufficient and necessary condition under which the ILQR is solvable. Different from the existed literature, we obtain the results in a novel way. In order to obtain a tighter necessary condition, we investigate the solution structure of a two-point boundary value problem for a stochastic differential equations directly but involve no complicated probabilistic derivation. Consider that there are close relationships between the linear game problem and H+∞ control and ILQR,the idea in the paper can also be extended to solve these problems.
引文
[1]J.Bismut,“Linear quadratic optimal stochastic control with random coefficients,”SIAM Journal on Control and Optimization,vol.14,no.3,pp.419–444,1976.
[2]M.Rami,J.Moore,and X.Zhou,“Indefinite stochastic linear quadratic control and generalized differential Riccati equation,”SIAM Journal on Control and Optimization,vol.40,no.4,pp.1296–1311,2002.
[3]S.Chen,X.Li,and X.Zhou,“Stochastic linear quadratic regulators with indefinite control weight costs,”SIAM Journal on Control and Optimization,vol.36,no.5,pp.1685–1702,1998.
[4]M.A.Rami and X.Y.Zhou,“Linear matrix inequalities,riccati equations,and indefinite stochastic linear quadratic controls,”IEEE Transactions on Automatic Control,vol.45,no.6,pp.1131–1143,2000.
[5]M.Ait Rami,X.Chen,J.B.Moore,and X.Y.Zhou,“Solvability and asymptotic behavior of generalized riccati equations arising in indefinite stochastic lq controls,”Automatic Control IEEE Transactions on,vol.46,no.3,pp.428–440,2001.
[6]W.M.Wonham,“On a matrix riccati equation of stochastic control,”SIAM Journal on Control,vol.6,no.4,pp.681–697,1968.
[7]A.Bensoussan,“Lecture on stochastic control,part I,”Lecture Notes in Math,vol.972,no.1,pp.1–39,1983.
[8]M.H.A.Davis,“Linear estimation and stochastic control,”Technometrics,vol.76,no.2,pp.192–193,1984.
[9]S.Chen and J.Yong,“Stochastic linear quadratic optimal control problems,”Applied Mathematics and Optimization,vol.43,no.1,pp.21–45,2001.
[10]J.Yong,“Linear Forward-Backward Stochastic Differential Equations,”Applied Mathematics and Optimization,vol.39,no.1,pp.93–119,1999.
[11]S.Peng and Z.Wu,“Fully coupled forward-backward stochastic differential equations and applications to optimal control,”SIAM Journal on Control&Optimization,vol.37,no.3,pp.825–843,1999.
[2]M.Rami,J.Moore,and X.Zhou,“Indefinite stochastic linear quadratic control and generalized differential Riccati equation,”SIAM Journal on Control and Optimization,vol.40,no.4,pp.1296–1311,2002.
[3]S.Chen,X.Li,and X.Zhou,“Stochastic linear quadratic regulators with indefinite control weight costs,”SIAM Journal on Control and Optimization,vol.36,no.5,pp.1685–1702,1998.
[4]M.A.Rami and X.Y.Zhou,“Linear matrix inequalities,riccati equations,and indefinite stochastic linear quadratic controls,”IEEE Transactions on Automatic Control,vol.45,no.6,pp.1131–1143,2000.
[5]M.Ait Rami,X.Chen,J.B.Moore,and X.Y.Zhou,“Solvability and asymptotic behavior of generalized riccati equations arising in indefinite stochastic lq controls,”Automatic Control IEEE Transactions on,vol.46,no.3,pp.428–440,2001.
[6]W.M.Wonham,“On a matrix riccati equation of stochastic control,”SIAM Journal on Control,vol.6,no.4,pp.681–697,1968.
[7]A.Bensoussan,“Lecture on stochastic control,part I,”Lecture Notes in Math,vol.972,no.1,pp.1–39,1983.
[8]M.H.A.Davis,“Linear estimation and stochastic control,”Technometrics,vol.76,no.2,pp.192–193,1984.
[9]S.Chen and J.Yong,“Stochastic linear quadratic optimal control problems,”Applied Mathematics and Optimization,vol.43,no.1,pp.21–45,2001.
[10]J.Yong,“Linear Forward-Backward Stochastic Differential Equations,”Applied Mathematics and Optimization,vol.39,no.1,pp.93–119,1999.
[11]S.Peng and Z.Wu,“Fully coupled forward-backward stochastic differential equations and applications to optimal control,”SIAM Journal on Control&Optimization,vol.37,no.3,pp.825–843,1999.