Solving Nonzero-Sum Nash Differential Game via Variation and Pseudospectral Methods

DOI

10.2991/iccse-15.2015.1How to use a DOI?

Keywords

Nonzero-sum Nash game, Differential game, Multi-player, Legendre Pseudospectral Method, SNOPT

Abstract

A numerical methods are presented in this paper to solve the nonzero-sum N-player Nash differential game. Variation methods are used to convert the original game into a regular optimal control problem which consists of one objective function, the state equations of all the players with initial conditions and the other necessary conditions derived. Then the later optimization problem is interpolated through the Legendre-pseudospectral method(LPM) and solved by applying SNOPT algorithm to get the optimal state trajectory. As an illustration, the air combat between a superior fighter and an inferior fighter is formulated as a nonzero-sum differential game. The states, traces, costs of both and the relative distance between them are displayed. The results show that numerical solutions converge to the saddle-points successfully, which show the feasibility and effectiveness of the proposed method in solving the nonzero-sum differential game.

Copyright

© 2015, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Guang-Yan Xu
AU  - Biao Zhou
AU  - Hong-Mei Zhang
AU  - Dan Zhao
PY  - 2015/07
DA  - 2015/07
TI  - Solving Nonzero-Sum Nash Differential Game via Variation and Pseudospectral Methods
BT  - Proceedings of the 2015 International Conference on Computational Science and Engineering
PB  - Atlantis Press
SP  - 1
EP  - 6
SN  - 2352-538X
UR  - https://doi.org/10.2991/iccse-15.2015.1
DO  - 10.2991/iccse-15.2015.1
ID  - Xu2015/07
ER  -