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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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems Vol. 29; no. 4; pp. 957 - 969
Main Authors: Wei, Qinglai, Liu, Derong, Lin, Qiao, Song, Ruizhuo
Format: Journal Article
Language:English
Published: United States IEEE 01.04.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:2162-237X
2162-2388
2162-2388
DOI:10.1109/TNNLS.2016.2638863