Interception in differential pursuit/evasion games

John A.  Morgan

doi:10.3934/jdg.2016018

Article Contents

2016, Volume 3, Issue 4: 335-354. Doi: 10.3934/jdg.2016018 open access

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Interception in differential pursuit/evasion games

John A. Morgan^1,

1.
The Aerospace Corporation, P. O. Box 92957, Los Angeles, CA 90009

Received: December 2013

Revised: March 2016

Published: October 2016

Abstract / Introduction Related Papers Cited by

Abstract

A qualitative criterion for a pursuer to intercept a target in a class of differential games is obtained in terms of future cones: Topological cones that contain all attainable trajectories of target or interceptor originating from an initial position. An interception solution exists after some initial time iff the future cone of the target lies within the future cone of the interceptor. The solution may be regarded as a kind of Nash equilibrium. This result is applied to two examples:
1. The game of Two Cars: The future cone condition is shown to be equivalent to conditions for interception obtained by Cockayne.
2. Satellite warfare: The future cone for a spacecraft or direct-ascent antisatellite weapon (ASAT) maneuvering in a central gravitational field is obtained and is shown to equal that for a spacecraft which maneuvers solely by means of a single velocity change at the cone vertex.
The latter result is illustrated with an analysis of the January 2007 interception of the FengYun-1C spacecraft.

Keywords:

Differential games,
pursuit/evasion games.

Mathematics Subject Classification: Primary: 49N75; Secondary: 91A23.

Citation:

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Cited by

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