Alternative Theorem for Differential Games with Strongly Convex Admissible Control Sets
A linear differential game with strongly convex admissible control sets and a smooth target set is considered. For such a differential game we obtain the alternative theorem. This theorem states that for any initial position either there is a program strategy of pursuer that guarantees the capture or there is a program strategy of evader that guarantees the evasion. This result is based on the commutativity of the Minkowski sum and difference for sets with special properties of strong and weak convexity in a Banach space.
KeywordsDifferential game Strongly convex set The Minkowski sum and difference
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