Approximate solution of singularly perturbed nonlinear pursuit-evasion games

A methodology to obtain an approximate solution of a singularly perturbed nonlinear differential game is presented. The outcome of the game with approximate strategies, defined as extended value, is related to the saddle-point value of the game. In an example of a simple pursuit-evasion game, it is shown that the proposed methodology leads to an easily implementable feedback form solution with fairly accurate results. This approach seems to be attractive for analyzing realistic air-combat models without solving a two-point boundary-value problem.This research was partially supported by AFSC Contract No. F-49620-79-6-0135. The authors are grateful to Prof. J. V. Breakwell for encouraging the approach taken in this research. Thanks are also due to Dr. S. Gutman and Dr. J. Lewin for their useful comments.