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Approximate Solution for Three-Player Mixed-Zero-Sum Nonlinear Game via ADP Structure

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Proceedings of 2017 Chinese Intelligent Systems Conference (CISC 2017)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 459))

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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.

The work was supported by National Natural Science Foundation of China (No. 61433003, No. 61573174, and No. 61273150).

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Author information

Authors and Affiliations

  1. School of Automation, Beijing Institute of Technology, Beijing, 100081, China

    Yongfeng Lv, Xuemei Ren, Qinqin Yang & Linwei Li

  2. Faculty of Mechanical & Electrical Engineering, Kunming University of Science & Technology, Kunming, 650500, China

    Jing Na

Authors
  1. Yongfeng Lv
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  2. Xuemei Ren
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  3. Jing Na
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  4. Qinqin Yang
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  5. Linwei Li
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Corresponding author

Correspondence to Xuemei Ren .

Editor information

Editors and Affiliations

  1. Beihang University , Beijing, China

    Yingmin Jia

  2. Beijing University of Posts and Telecommunications, Beijing, China

    Junping Du

  3. University of Science and Technology Beijing, Beijing, China

    Weicun Zhang

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© 2018 Springer Nature Singapore Pte Ltd.

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Lv, Y., Ren, X., Na, J., Yang, Q., Li, L. (2018). Approximate Solution for Three-Player Mixed-Zero-Sum Nonlinear Game via ADP Structure. In: Jia, Y., Du, J., Zhang, W. (eds) Proceedings of 2017 Chinese Intelligent Systems Conference. CISC 2017. Lecture Notes in Electrical Engineering, vol 459. Springer, Singapore. https://doi.org/10.1007/978-981-10-6496-8_33

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  • DOI: https://doi.org/10.1007/978-981-10-6496-8_33

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-6495-1

  • Online ISBN: 978-981-10-6496-8

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