A zero-sum electromagnetic evader–interrogator differential game with uncertainty

Abstract

We consider dynamic electromagnetic evasion-interrogation games in which the evader can use ferroelectric material coatings to attempt to avoid detection while the interrogator can manipulate the interrogating frequencies to enhance detection. The resulting problem is formulated as a two-player zero-sum dynamic differential game in which the cost functional is based on the expected value of the intensity of the reflected signal. We show that there exists a saddle point for the relaxed form of this dynamic differential game in which the relaxed controls appear bilinearly in the dynamics governed by a partial differential equation. We also present a computational framework for construction of approximate saddle point strategies in feedback form for a special case of this relaxed differential game with strategies and payoff in the sense of Berkovitz.

Keywords:

• electromagnetic evasion pursuit
• uncertainty
• differential games
• theory and approximation
• backward Kolmogorov equations

AMS Subject Classifications::

• 83C50
• 91A23
• 49N70
• 49N90
• 65M32
• 68T37
• 60J70

Acknowledgements

This research was supported in part by the U.S. Air Force Office of Scientific Research under grant number FA9550-09-1-0226. The authors wish to dedicate this article to the late L.D. Berkovitz who served, until his death in October 2009, as mentor and life long friend to the first author. He is missed greatly by his many friends, colleagues and extended family.