Geodesic
One problem on stable tracking of motion
Trudy Instituta matematiki i mehaniki, Dynamical systems: modeling, optimization, and control, Tome 12 (2006) no. 1, pp. 142-156 Cet article a éte moissonné depuis la source Math-Net.Ru

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A problem about tracking of a model motion by motion of an object under conditions of uncertainty or conflict [1–7] is considered. Controls are formed in a time-discrete scheme on the basis of step-by-step probabilistic tests. 
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N. N. Krasovskii; A. N. Kotel'nikova. One problem on stable tracking of motion. Trudy Instituta matematiki i mehaniki, Dynamical systems: modeling, optimization, and control, Tome 12 (2006) no. 1, pp. 142-156. http://geodesic.mathdoc.fr/item/TIMM_2006_12_1_a10/

[1] Osipov Yu. S., “K teorii differentsialnykh igr sistem s posledeistviem”, Prikl. matematika i mekhanika, 35:2 (1971), 300–311 | MR | Zbl

[2] Kurzhanskii A. B., Upravlenie i nablyudenie v usloviyakh neopredelennosti, Nauka, M., 1977 | MR | Zbl

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

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

[5] Subbotin A. I., Obobschennye resheniya uravnenii v chastnykh proizvodnykh pervogo poryadka. Perspektivy dinamicheskoi optimizatsii, Institut kompyut. issled., Moskva–Izhevsk, 2003 | Zbl

[6] Kolmanovskii V. B., Nosov V. R., Ustoichivost i periodicheskie rezhimy reguliruemykh sistem s posledeistviem, Nauka, M., 1981 | MR

[7] Aizeks R., Differentsialnye igry, Mir, M., 1967, 479 pp. | MR

[8] Ito K., Makkin G., Diffuzionnye protsessy i ikh traektorii, perev. s angl., Mir, M., 1968 | Zbl

[9] Ito K., Nisio M., “On stationary solutions of stochastic differential equations”, J. Math. Kyoto Univ., 4:1 (1964), 1–79 | MR

[10] Harold J. Kushner., Stochastic Stability and Control, Academic Press, New York, 1967 | MR | Zbl

[11] Liptser R. Sh., Shiryaev A. N., Statistika sluchainykh protsessov, Nauka, M., 1974 | MR | Zbl

[12] Khasminskii R. Z., Ustoichivost sistem differentsialnykh uravnenii pri sluchainykh vozmuscheniyakh ikh parametrov, Gl. red. fiz.-mat. lit., Moskva, 1969

[13] Dynkin E. B., Markovskie protsessy, Fizmatgiz, 1963 | MR

[14] Osipov Yu. S., “O stabilizatsii upravlyaemykh sistem s zapazdyvaniem”, Differents. uravneniya, 1:5 (1965), 463–473

[15] Krasovskii N. N., Osipov Yu. S., “O stabilizatsii dvizhenii upravlyaemogo ob'ekta s zapazdyvaniem v sisteme regulirovaniya”, Izv. AN SSSR. Tekhn. kibernetika, 1963, no. 6, 3–15 | MR | Zbl

[16] Kheil Dzh., Teoriya funktsionalno-differentsialnykh uravnenii, Mir, M., 1984 | MR

[17] Shimanov S. N., “K teorii lineinykh differentsialnykh uravnenii s posledeistviem”, Differents. uravneniya, 1:1 (1965), 102–116 | Zbl

[18] Kats I. Ya., Krasovskii N. N., “Ob ustoichivosti sistem so sluchainymi parametrami”, Prikl. matematika i mekhanika, 24:5 (1960), 809–823 | Zbl

[19] Kats I. Ya. and Martynyuk A. A., Stability and Stabilization of Nonlinear Systems with Random Structure, Taylor and Francis Inc., London and New York, 2002 | MR

[20] Lyapunov A. M., Obschaya zadacha ob ustoichivosti dvizheniya, Gostekhizdat, M., 1950

[21] Malkin I. G., Teoriya ustoichivosti dvizheniya, Izd-e vtoroe, ispravlennoe, Nauka, M., 1966 | MR | Zbl

[22] Krasovskii N. N., Nekotorye zadachi teorii ustoichivosti dvizheniya, Fizmatgiz, M., 1959 | MR

[23] Subbotin A. I., “Ekstremalnye strategii v differentsialnykh igrakh s polnoi pamyatyu”, Dokl. AN SSSR, 206:3 (1972), 552–555 | MR | Zbl

[24] Lukoyanov N. Yu., “Ob ekstremalnom pritselivanii v zadachakh upravleniya sistemami s posledeistviem”, Izv. UrGU, 26:5 (2003), 115–123, Matematika. Mekhanika. Informatika | MR

[25] Lukoyanov N. Yu., Reshetova T. N., “Zadachi konfliktnogo upravleniya funktsionalnymi sistemami vysokoi razmernosti”, Prikl. matematika i mekhanika, 62:4 (1998), 586–597 | MR

[26] Repin Yu. M., “Kvadratichnye funktsionaly Lyapunova dlya sistem s zapazdyvaniem”, Prikl. matematika i mekhanika, 29:3 (1965), 564–566 | MR | Zbl

[27] Kim A. V., $i$-Gladkii analiz i funktsionalno-differentsialnye uravneniya, Ekaterinburg, 1996

[28] Yoshizawa T., “Stability Theory by Lyapunov's Second Method”, Math. Soc. Japan, 9, The Mathematical Society of Japan, Tokyo, 1966 | MR | Zbl

[29] fon Neiman Dzh., Morgenshtern O., Teoriya igr i ekonomicheskoe povedenie, Nauka, M., 1970 | MR

[30] Ito K., “Ob odnoi formule, kasayuscheisya stokhasticheskikh differentsialov”, Matematika. Sb. perev. inostr. statei, 3:5 (1959), 131–141