Zero-Sum Differential Games for Nonlinear Systems Using Adaptive Dynamic Programming with Input Constraint
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- 英文论文题名：Zero-Sum Differential Games for Nonlinear Systems Using Adaptive Dynamic Programming with Input Constraint
- 论文作者：Jingliang Sun ; Chunsheng Liu
- 英文论文作者：Jingliang Sun ; Chunsheng Liu ; College of Automation Engineering ; Nanjing University of Aeronautics and Astronautics
- 年：2017
- 作者机构：College of Automation Engineering,Nanjing University of Aeronautics and Astronautics;
- 英文论文关键词：differential game ; adaptive dynamic programming ; asymptotically stability ; input constraints
- 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：TP273
- 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：269k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, the zero-sum differential game problem for a class of nonlinear system with input constraints is investigated via adaptive dynamic programming(ADP). A suitable non-quadratic functional is utilized to embed the control constraints into the differential game problem. Then, the Nash equilibrium solution is found by solving the constrained Hamilton-Jacobi-Isaacs(HJI) equation. The single critic network is constructed to approximate the solution of associated HJI equation online. A robustifying control term is added to the controller to eliminate the effect of residual error, leading to the asymptotically stability of the closed-loop system. Simulation results verify the effectiveness of proposed method by using a simple nonlinear system.
In this paper, the zero-sum differential game problem for a class of nonlinear system with input constraints is investigated via adaptive dynamic programming(ADP). A suitable non-quadratic functional is utilized to embed the control constraints into the differential game problem. Then, the Nash equilibrium solution is found by solving the constrained Hamilton-Jacobi-Isaacs(HJI) equation. The single critic network is constructed to approximate the solution of associated HJI equation online. A robustifying control term is added to the controller to eliminate the effect of residual error, leading to the asymptotically stability of the closed-loop system. Simulation results verify the effectiveness of proposed method by using a simple nonlinear system.
In this paper, the zero-sum differential game problem for a class of nonlinear system with input constraints is investigated via adaptive dynamic programming(ADP). A suitable non-quadratic functional is utilized to embed the control constraints into the differential game problem. Then, the Nash equilibrium solution is found by solving the constrained Hamilton-Jacobi-Isaacs(HJI) equation. The single critic network is constructed to approximate the solution of associated HJI equation online. A robustifying control term is added to the controller to eliminate the effect of residual error, leading to the asymptotically stability of the closed-loop system. Simulation results verify the effectiveness of proposed method by using a simple nonlinear system.
引文
[1]Q.Wei,R.Song,and P.Yan,Data-driven zero-sum neuro-optimal control for a class of continuous-time unknown nonlinear systems with disturbance using ADP,IEEE Transactions on Neural Networks and Learning Systems,27(2):444-58,2016.
[2]D.Vrabie and F.Lewis,Adaptive dynamic programming for online solution of a zero-sum differential game,Journal of Control Theory and Applications,9(3):353-360,2011.
[3]H.Zhang,Q.Wei,and D.Liu,An iterative adaptive dynamic programming method for solving a class of nonlinear zero-sum differential games,Automatica,47(1):207-214,2011.
[4]K.Vamvoudakis,D.Vrabie,and F.Lewis,Adaptive optimal control algorithm for zero-sum Nash games with integral reinforcement learning,in AIAA Guidance,Navigation,and Control Conference,Minneapolis,Minnesota,2012:4773.
[5]J.Sun,C.Liu,and Q.Ye,Robust differential game guidance laws design for uncertain interceptor-target engagement via adaptive dynamic programming,International Journal of Control,90(5):990-1004,2017.
[6]M.Abu-Khalaf,F.L.Lewis,and H.Jie,Neurodynamic programming and zero-sum games for constrained control systems,IEEE Transactions on Neural Networks,19(7):1243-1252,2008.
[7]H.Modares,F.L.Lewis,and M.-B.N.Sistani,Online solution of nonquadratic two-player zero-sum games arising in the H control of constrained input systems,International Journal of Adaptive Control and Signal Processing,28(3-5):232-254,2014.
[8]D.Wang,C.Mu,Q.Zhang,and D.Liu,Event-based input-constrained nonlinear H state feedback with adaptive critic and neural implementation,Neurocomputing,214:848-856,2016.
[9]D.Liu,X.Yang,D.Wang,and Q.Wei,Reinforcement-learning-based robust controller design for continuous-time uncertain nonlinear systems subject to input constraints,IEEE Transactions on Cybernetics,45(7):1372-1385,2015.
[10]X.Yang,D.Liu,and Y.Huang,Neural-network-based online optimal control for uncertain non-linear continuous-time systems with control constraints,IET Control Theory&Applications,7(17):2037-2047,2013.
[11]D.Wang,D.Liu,H.Li,and H.Ma,Neural-network-based robust optimal control design for a class of uncertain nonlinear systems via adaptive dynamic programming,Information Sciences,282(0):167-179,2014.
[12]H.Xu,Finite-horizon near optimal design of nonlinear two-player zero-sum game in presence of completely unknown dynamics,Journal of Control,Automation and Electrical Systems,26(4):361-370,2015.
[2]D.Vrabie and F.Lewis,Adaptive dynamic programming for online solution of a zero-sum differential game,Journal of Control Theory and Applications,9(3):353-360,2011.
[3]H.Zhang,Q.Wei,and D.Liu,An iterative adaptive dynamic programming method for solving a class of nonlinear zero-sum differential games,Automatica,47(1):207-214,2011.
[4]K.Vamvoudakis,D.Vrabie,and F.Lewis,Adaptive optimal control algorithm for zero-sum Nash games with integral reinforcement learning,in AIAA Guidance,Navigation,and Control Conference,Minneapolis,Minnesota,2012:4773.
[5]J.Sun,C.Liu,and Q.Ye,Robust differential game guidance laws design for uncertain interceptor-target engagement via adaptive dynamic programming,International Journal of Control,90(5):990-1004,2017.
[6]M.Abu-Khalaf,F.L.Lewis,and H.Jie,Neurodynamic programming and zero-sum games for constrained control systems,IEEE Transactions on Neural Networks,19(7):1243-1252,2008.
[7]H.Modares,F.L.Lewis,and M.-B.N.Sistani,Online solution of nonquadratic two-player zero-sum games arising in the H control of constrained input systems,International Journal of Adaptive Control and Signal Processing,28(3-5):232-254,2014.
[8]D.Wang,C.Mu,Q.Zhang,and D.Liu,Event-based input-constrained nonlinear H state feedback with adaptive critic and neural implementation,Neurocomputing,214:848-856,2016.
[9]D.Liu,X.Yang,D.Wang,and Q.Wei,Reinforcement-learning-based robust controller design for continuous-time uncertain nonlinear systems subject to input constraints,IEEE Transactions on Cybernetics,45(7):1372-1385,2015.
[10]X.Yang,D.Liu,and Y.Huang,Neural-network-based online optimal control for uncertain non-linear continuous-time systems with control constraints,IET Control Theory&Applications,7(17):2037-2047,2013.
[11]D.Wang,D.Liu,H.Li,and H.Ma,Neural-network-based robust optimal control design for a class of uncertain nonlinear systems via adaptive dynamic programming,Information Sciences,282(0):167-179,2014.
[12]H.Xu,Finite-horizon near optimal design of nonlinear two-player zero-sum game in presence of completely unknown dynamics,Journal of Control,Automation and Electrical Systems,26(4):361-370,2015.