Abstract
In this chapter, a synchronous solution method for multi-player zero-sum (ZS) games without system dynamics is established based on neural network. The policy iteration (PI) algorithm is presented to solve the Hamilton–Jacobi–Bellman (HJB) equation. It is proven that the obtained iterative cost function is convergent to the optimal game value. For avoiding system dynamics, off-policy learning method is given to obtain the iterative cost function, controls and disturbances based on PI. Critic neural network (CNN), action neural networks (ANNs) and disturbance neural networks (DNNs) are used to approximate the cost function, controls and disturbances. The weights of neural networks compose the synchronous weight matrix, and the uniformly ultimately bounded (UUB) of the synchronous weight matrix is proven. Two examples are given to show that the effectiveness of the proposed synchronous solution method for multi-player ZS games.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Yeung, D., Petrosyan, L.: Cooperative Stochastic Differential Games. Springer, Berlin (2006)
Lewis, F., Vrabie, D., Syrmos, V.: Optimal Control, 3rd edn. Wiley, Hoboken (2012)
Song, R., Lewis, F., Wei, Q.: Off-policy integral reinforcement learning method to solve nonlinear continuous-time multi-player non-zero-sum games. IEEE Trans. Neural Networks Learn. Syst. 28(3), 704–713 (2016)
Liu, D., Wei, Q.: Multiperson zero-sum differential games for a class of uncertain nonlinear systems. Int. J. Adap. Control Signal Process. 28(3–5), 205–231 (2014)
Mu, C., Sun, C., Song, A., Yu, H.: Iterative GDHP-based approximate optimal tracking control for a class of discrete-time nonlinear systems. Neurocomputing 214(19), 775–784 (2016)
Fang, X., Zheng, D., He, H., Ni, Z.: Data-driven heuristic dynamic programming with virtual reality. Neurocomputing 166(20), 244–255 (2015)
Feng, T., Zhang, H., Luo, Y., Zhang, J.: Stability analysis of heuristic dynamic programming algorithm for nonlinear systems. Neurocomputing 149(Part C, 3), 1461–1468 (2015)
Feng, T., Zhang, H., Luo, Y., Liang, H.: Globally optimal distributed cooperative control for general linear multi-agent systems. Neurocomputing 203(26), 12–21 (2016)
Lewis, F., Vrabie, D., Syrmos, V.: Optimal Control. Wiley, NewYork (2012)
Basar, T., Olsder, G.: Dynamic Noncooperative Game Theory. Academic Press, New York (1982)
Vamvoudakis, K., Lewis, F.: Multi-player non-zero-sum games: online adaptive learning solution of coupled Hamilton-Jacobi equations. Automatica 47(8), 1556–1569 (2011)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Science Press, Beijing and Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Song, R., Wei, Q., Li, Q. (2019). Neural-Network-Based Synchronous Iteration Learning Method for Multi-player Zero-Sum Games. In: Adaptive Dynamic Programming: Single and Multiple Controllers. Studies in Systems, Decision and Control, vol 166. Springer, Singapore. https://doi.org/10.1007/978-981-13-1712-5_11
Download citation
DOI: https://doi.org/10.1007/978-981-13-1712-5_11
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-1711-8
Online ISBN: 978-981-13-1712-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)