@inproceedings{2cee5180e22044c08ee47a9713462ea9,
title = "Approximate solution for three-player mixed-zero-sum nonlinear game via ADP structure",
abstract = "In this paper, a three-player mixed-zero-sum game situation with nonlinear dynamics is proposed, and an approximate dynamic programming (ADP) learning scheme is used to solve the proposed problem. First, the problem formulation is presented. A value function for player 1 and 2 nonzero-sum game is constructed, another value function for player 1 and 3 zero-sum game is presented for three-player nonlinear game system. Because of the difficulty to solve the nonlinear Hamilton-Jacobi (HJ) equation, the single-layer critic neural networks are used to approximate the optimal value functions. Then the approximated critic neural networks (NNs) are directly used to learn the optimal solutions for three-player mixed-zero-sum nonlinear game. A novel adaptive law with the estimation performance index is proposed to estimate the unknown coefficient vector. Finally, a simulation example is presented to illustrate the proposed methods.",
keywords = "Approximate dynamic programming, Neural networks, Parameter estimation, Zero-sum game",
author = "Yongfeng Lv and Xuemei Ren and Jing Na and Qinqin Yang and Linwei Li",
note = "Publisher Copyright: {\textcopyright} 2018, Springer Nature Singapore Pte Ltd.; Chinese Intelligent Systems Conference, CISC 2017 ; Conference date: 14-10-2017 Through 15-10-2017",
year = "2018",
doi = "10.1007/978-981-10-6496-8_33",
language = "English",
isbn = "9789811064951",
series = "Lecture Notes in Electrical Engineering",
publisher = "Springer Verlag",
pages = "351--361",
editor = "Junping Du and Weicun Zhang and Yingmin Jia",
booktitle = "Proceedings of 2017 Chinese Intelligent Systems Conference",
address = "Germany",
}