Geodesic
Linear differential games with impulse control of players
Trudy Instituta matematiki i mehaniki, Dynamical systems and control problems, Tome 11 (2005) no. 1, pp. 212-224 
A. A. Chikrii; I. I. Matichin. Linear differential games with impulse control of players. Trudy Instituta matematiki i mehaniki, Dynamical systems and control problems, Tome 11 (2005) no. 1, pp. 212-224. http://geodesic.mathdoc.fr/item/TIMM_2005_11_1_a18/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider pursuit games in which players (the pursuer, evader or both players) use impulse controls, which is expressed in terms of the Dirac delta-function. We study linear dynamical system described by ordinary differential equations whose trajectories have discontinuities at discrete time instants. Such systems are a kind of hybrid ones. The research is based on the principal ideas of the decision function method. The following cases are considered successively: impulse control of the pursuer; impulse control of the evader; impulse control of both players. For each of the three cases, the problem of approach to a cylindrical terminal set is studied and sufficient solvability conditions for the above problem are obtained. The theoretical results are illustrated with an example of a pursuit game with simple motion.

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