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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] Krasovskii N. N., Teoriya upravleniya dvizheniem, Nauka, M., 1968, 476 pp. | MR

[2] Krasovskii N. N., Igrovye zadachi o vstreche dvizhenii, Nauka, M., 1970, 420 pp. | MR

[3] Krasovskii N. N., Upravlenie dinamicheskoi sistemoi, Nauka, M., 1985, 520 pp. | MR

[4] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974, 455 pp. | MR | Zbl

[5] Subbotin A. I., Chentsov A. G., Optimizatsiya garantii v zadachakh upravleniya, Nauka, M., 1981, 288 pp. | MR

[6] Pontryagin L. S., Izbrannye nauchnye trudy, T. 2, Nauka, M., 1988, 576 pp. | MR

[7] Chikrii A. A., Konfliktno upravlyaemye protsessy, Nauk. dumka, Kiev, 1992, 384 pp.

[8] Mikusinskii Ya., Sikorskii R., Elementarnaya teoriya obobschennykh funktsii, Inostr. literatura, M., 1959, 79 pp.

[9] Filippov A. F., Differentsialnye uravneniya s razryvnoi pravoi chastyu, Nauka, M., 1985, 224 pp. | MR

[10] Ioffe A. D., Tikhomirov V. M., Teoriya ekstremalnykh zadach, Nauka, M., 1974, 480 pp. | MR | Zbl

[11] Aumann R. J., “Integrals of set valued functions”, J. Math. Anal. Appl., 12 (1965), 1–12 | DOI | MR | Zbl

[12] Chikrii A. A., Eidelman S. D., “Obobschennye matrichnye funktsii Mittag-Lefflera v igrovykh zadachakh dlya evolyutsionnykh uravnenii drobnogo poryadka”, Kibernetika i sistemnyi analiz, 2000, no. 3, 3–32 | MR | Zbl