Discriminating domains in differential games.

Summary This thesis is devoted to a differential game - that is, a dual-control differential system in which one player seeks to move the state of the system into a given target while the other player seeks to keep the state of the system off the target. This is the target game. We study this game in the context of non-anticipatory strategies (by Elliot & Kalton) and feedback strategies (by Breakwell & Bernhard). For each strategy context, we define victory domains, which are the initial data sets from which a player can win regardless of the opponent's action. We show, in the context of non-anticipatory strategies, that the victory domains form a partition of the target's complement. We characterize the victory domains of each player using a set (the discriminant kernel) defined from geometric conditions inspired by viability theory (c. F. J. P. Aubin). Thanks to this characterization, we highlight a barrier property on the edge of the victory domains. We propose algorithms for computing victory domains that do not require the computation of trajectories.