Pursuit-Evasion Games with Impulsive Dynamics
In this chapter, we investigate a two-player zero-sum game with separated impulsive dynamics. We study both qualitative and quantitative games. For the qualitative games, we provide a geometrical characterization of the victory domains. For the quantitative games, we characterize the value functions using the Isaacs partial differential inequalities. As a by-product, we obtain a new result of existence of a value for impulsive differential games. The main tool of our approach is the notion of impulse discriminating domain, which is introduced and discussed extensively here.
KeywordsDifferential Game SIAM Journal Viability Kernel Impulse System Impulsive Dynamics
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- J.-P. Aubin. Viability Theory. Systems & Control: Foundations & Applications. Birkhäuser, Boston, 1991.Google Scholar
- P. Cardaliaguet, M. Quincampoix, and P. Saint-Pierre. Numerical Methods for Differential Games. In M. Bardi, T.E.S. Raghavan, and T. Parthasarathy, editors, Stochastic and Differential Games: Theory and Numerical Methods, Annals of the International Society of Dynamic Games, pages 177–247. (Birkhäuser), 1999.Google Scholar
- R.J. Elliott and N.J. Kalton. The Existence of Value in Differential Games of Pursuit and Evasion. Journal of Differential Equations, (12):504–523, 1972.Google Scholar
- P. Varaiya. Differential Games with Dynamical Systems. In H.W. Kuhn and G.P. Szeg, editors, Differential Games and Related Topics, pages 129–144. North-Holland Publishing Company, Amsterdam, 1971.Google Scholar