Approximate solution for three-player mixed-zero-sum nonlinear game via ADP structure

Yongfeng Lv, Xuemei Ren*, Jing Na, Qinqin Yang, Linwei Li

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publicationProceedings of 2017 Chinese Intelligent Systems Conference
EditorsJunping Du, Weicun Zhang, Yingmin Jia
PublisherSpringer Verlag
Pages351-361
Number of pages11
ISBN (Print)9789811064951
DOIs
Publication statusPublished - 2018
EventChinese Intelligent Systems Conference, CISC 2017 - Mudanjiang, China
Duration: 14 Oct 201715 Oct 2017

Publication series

NameLecture Notes in Electrical Engineering
Volume459
ISSN (Print)1876-1100
ISSN (Electronic)1876-1119

Conference

ConferenceChinese Intelligent Systems Conference, CISC 2017
Country/TerritoryChina
CityMudanjiang
Period14/10/1715/10/17

Keywords

  • Approximate dynamic programming
  • Neural networks
  • Parameter estimation
  • Zero-sum game

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