Geodesic
On the theory of three-person differential games
Trudy Instituta matematiki i mehaniki, Dynamical systems: modeling, optimization, and control, Tome 12 (2006) no. 1, pp. 78-85 
N. L. Grigorenko. On the theory of three-person differential games. Trudy Instituta matematiki i mehaniki, Dynamical systems: modeling, optimization, and control, Tome 12 (2006) no. 1, pp. 78-85. http://geodesic.mathdoc.fr/item/TIMM_2006_12_1_a6/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A differential game of three players with dynamics described by linear differential equations under geometric constraints on the control parameters is considered. Sufficient conditions are obtained for the existence of the first player's strategy guaranteeing that the trajectory of the game reaches a given target set for any admissible control of the second player and avoids the terminal set of the third player. An algorithm of constructing the first player's strategy guaranteeing the game's termination in finite time is suggested. A solution of a model example is given.

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

[2] Blagodatskikh V. I., Vvedenie v optimalnoe upravlenie, Vysshaya shkola, M., 2001

[3] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1969

[4] Osipov Yu. S., Vasilev F. P., Potapov M. M., Osnovy metoda dinamicheskoi regulyarizatsii, Izd-vo MGU, M., 1999

[5] Pontryagin L. S., Mischenko E. F., “Zadacha ob uklonenii ot vstrechi v lineinykh differentsialnykh igrakh”, Differents. uravneniya, 7:3 (1971), 436–445 | Zbl

[6] Polovinkin E. S., Balashov M. V., Elementy vypuklogo analiza, Fizmatlit, M., 2004

[7] Kryazhimskii A. V., Osipov Yu. S., “Metod ekstremalnogo sdviga i zadachi optimizatsii”, Tr. In-ta matematiki i mekhaniki UrO RAN, 10, no. 2, Ekaterinburg, 2004, 83–105

[8] Nikolskii M. S., “Nekotorye zadachi otslezhivaniya zadannogo dvizheniya pri nalichii pomekh”, Differents. uravneniya, 31:11 (1995), 1866–1873 | MR

[9] Grigorenko N. L., Matematicheskie metody upravleniya neskolkimi dinamicheskimi protsessami, Izd-vo MGU, M., 1990