Problems of pursuit and evasion

Abstract

Problems of pursuit and evasion play significant part in naval warfare - particularly in ASW. They are of no less importance in aerial warfare and are now becoming important in space. Their practical importance has given rise to a great many studies in both the USA and the USSR. The latter were little known until two or three years ago since when they have become more and more available in translation. This has revealed that the Soviet development has been so great that the eminent mathematician Pontryagin leads a complete school on the subject. Among other things he has discovered a "Maximum principle" that bears his name. This report presents an analysis of the work of the Pontryagin school in its relation to ASW and its relation to other work in the same field - especially to that of the great Swedish probabilist: U. Grenander.