Adaptive Dynamic Programming for Discrete-Time Zero-Sum Games

In this paper, a novel adaptive dynamic programming (ADP) algorithm, called "iterative zero-sum ADP algorithm," is developed to solve infinite-horizon discrete-time two-player zero-sum games of nonlinear systems. The present iterative zero-sum ADP algorithm permits arbitrary positive semid...

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Vydané v:	IEEE transaction on neural networks and learning systems Ročník 29; číslo 4; s. 957 - 969
Hlavní autori:	Wei, Qinglai, Liu, Derong, Lin, Qiao, Song, Ruizhuo
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	United States IEEE 01.04.2018 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	Adaptive algorithms Adaptive critic designs adaptive dynamic programming (ADP) Algorithms approximate dynamic programming Computer simulation Convergence Dynamic programming Equilibrium Game theory Games Iterative algorithms neurodynamic programming Nonlinear systems Optimal control Performance analysis Performance indices Saddle points zero-sum game
ISSN:	2162-237X, 2162-2388, 2162-2388
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Abstract	In this paper, a novel adaptive dynamic programming (ADP) algorithm, called "iterative zero-sum ADP algorithm," is developed to solve infinite-horizon discrete-time two-player zero-sum games of nonlinear systems. The present iterative zero-sum ADP algorithm permits arbitrary positive semidefinite functions to initialize the upper and lower iterations. A novel convergence analysis is developed to guarantee the upper and lower iterative value functions to converge to the upper and lower optimums, respectively. When the saddle-point equilibrium exists, it is emphasized that both the upper and lower iterative value functions are proved to converge to the optimal solution of the zero-sum game, where the existence criteria of the saddle-point equilibrium are not required. If the saddle-point equilibrium does not exist, the upper and lower optimal performance index functions are obtained, respectively, where the upper and lower performance index functions are proved to be not equivalent. Finally, simulation results and comparisons are shown to illustrate the performance of the present method.
AbstractList	In this paper, a novel adaptive dynamic programming (ADP) algorithm, called "iterative zero-sum ADP algorithm," is developed to solve infinite-horizon discrete-time two-player zero-sum games of nonlinear systems. The present iterative zero-sum ADP algorithm permits arbitrary positive semidefinite functions to initialize the upper and lower iterations. A novel convergence analysis is developed to guarantee the upper and lower iterative value functions to converge to the upper and lower optimums, respectively. When the saddle-point equilibrium exists, it is emphasized that both the upper and lower iterative value functions are proved to converge to the optimal solution of the zero-sum game, where the existence criteria of the saddle-point equilibrium are not required. If the saddle-point equilibrium does not exist, the upper and lower optimal performance index functions are obtained, respectively, where the upper and lower performance index functions are proved to be not equivalent. Finally, simulation results and comparisons are shown to illustrate the performance of the present method. In this paper, a novel adaptive dynamic programming (ADP) algorithm, called "iterative zero-sum ADP algorithm," is developed to solve infinite-horizon discrete-time two-player zero-sum games of nonlinear systems. The present iterative zero-sum ADP algorithm permits arbitrary positive semidefinite functions to initialize the upper and lower iterations. A novel convergence analysis is developed to guarantee the upper and lower iterative value functions to converge to the upper and lower optimums, respectively. When the saddle-point equilibrium exists, it is emphasized that both the upper and lower iterative value functions are proved to converge to the optimal solution of the zero-sum game, where the existence criteria of the saddle-point equilibrium are not required. If the saddle-point equilibrium does not exist, the upper and lower optimal performance index functions are obtained, respectively, where the upper and lower performance index functions are proved to be not equivalent. Finally, simulation results and comparisons are shown to illustrate the performance of the present method.In this paper, a novel adaptive dynamic programming (ADP) algorithm, called "iterative zero-sum ADP algorithm," is developed to solve infinite-horizon discrete-time two-player zero-sum games of nonlinear systems. The present iterative zero-sum ADP algorithm permits arbitrary positive semidefinite functions to initialize the upper and lower iterations. A novel convergence analysis is developed to guarantee the upper and lower iterative value functions to converge to the upper and lower optimums, respectively. When the saddle-point equilibrium exists, it is emphasized that both the upper and lower iterative value functions are proved to converge to the optimal solution of the zero-sum game, where the existence criteria of the saddle-point equilibrium are not required. If the saddle-point equilibrium does not exist, the upper and lower optimal performance index functions are obtained, respectively, where the upper and lower performance index functions are proved to be not equivalent. Finally, simulation results and comparisons are shown to illustrate the performance of the present method.
Author	Wei, Qinglai Lin, Qiao Liu, Derong Song, Ruizhuo
Author_xml	– sequence: 1 givenname: Qinglai orcidid: 0000-0001-7002-9800 surname: Wei fullname: Wei, Qinglai email: qinglai.wei@ia.ac.cn organization: The State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China – sequence: 2 givenname: Derong orcidid: 0000-0003-3715-4778 surname: Liu fullname: Liu, Derong email: derong@ustb.edu.cn organization: School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China – sequence: 3 givenname: Qiao surname: Lin fullname: Lin, Qiao email: linqiao2014@ia.ac.cn organization: The State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China – sequence: 4 givenname: Ruizhuo surname: Song fullname: Song, Ruizhuo email: ruizhuosong@ustb.edu.cn organization: School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China
BackLink	https://www.ncbi.nlm.nih.gov/pubmed/28141530$$D View this record in MEDLINE/PubMed
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Snippet	In this paper, a novel adaptive dynamic programming (ADP) algorithm, called "iterative zero-sum ADP algorithm," is developed to solve infinite-horizon... In this paper, a novel adaptive dynamic programming (ADP) algorithm, called “iterative zero-sum ADP algorithm,” is developed to solve infinite-horizon...
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SubjectTerms	Adaptive algorithms Adaptive critic designs adaptive dynamic programming (ADP) Algorithms approximate dynamic programming Computer simulation Convergence Dynamic programming Equilibrium Game theory Games Iterative algorithms neurodynamic programming Nonlinear systems Optimal control Performance analysis Performance indices Saddle points zero-sum game
Title	Adaptive Dynamic Programming for Discrete-Time Zero-Sum Games
URI	https://ieeexplore.ieee.org/document/7835683 https://www.ncbi.nlm.nih.gov/pubmed/28141530 https://www.proquest.com/docview/2015121556 https://www.proquest.com/docview/1863706922
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