Yu. S. Osipov's work in mathematical control theory

A. V. Kryazhimskii

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 61 (2006) no. 4, pp. 593-610

Résumé

This paper gives an overview of Yu. S. Osipov's work in mathematical control theory, including development of the theory of positional differential games for control systems with time delay; analysis of the phenomenon of infinite dimensionality of the state space of a dynamical system in the context of differential games; development of the theory of dynamical inversion (dynamical regularization) for finite- and infinite-dimensional control systems; applications of methods of the theory of positional differential games beyond the scope of the theory itself; work on new differential-game methods and on methods of control under incomplete information. The author of this overview is the first student of Osipov, and also his longstanding colleague.

Bibliographie

[1] Yu. S. Osipov, “Alternativa v differentsialno-raznostnoi igre”, Dokl. AN SSSR, 197:5 (1971), 1022–1025 | MR | Zbl

[2] Yu. S. Osipov, “Differentsialnaya igra navedeniya dlya sistem s posledeistviem”, Prikl. matem. i mekh., 35:1 (1971), 123–131 | MR | Zbl

[3] Yu. S. Osipov, “Differentsialnye igry sistem s posledeistviem”, Dokl. AN SSSR, 196:4 (1971), 779–782 | MR | Zbl

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

[5] N. N. Krasovskii, Yu. S. Osipov, “Lineinye differentsialno-raznostnye igry”, Dokl. AN SSSR, 197:4 (1971), 777–780 | MR | Zbl

[6] Yu. S. Osipov, “Ob usloviyakh stabilnosti pogloscheniya v differentsialno-raznostnykh igrakh. I”, Upravlyaemye sistemy. Novosibirsk, 1971, no. 8, 13–20

[7] Yu. S. Osipov, “Ob usloviyakh stabilnosti pogloscheniya v differentsialno-raznostnykh igrakh. II”, Upravlyaemye sistemy. Novosibirsk, 1971, no. 8, 21–28 | MR

[8] Yu. S. Osipov, “Minimaksnoe pogloschenie v differentsialno-raznostnykh igrakh”, Dokl. AN SSSR, 203:1 (1972), 32–35 | MR | Zbl

[9] Yu. S. Osipov, V. G. Pimenov, “K teorii differentsialnykh igr v sistemakh s posledeistviem”, Prikl. matem. i mekh., 42:6 (1978), 969–977 | MR | Zbl

[10] A. V. Kryazhimskii, Yu. S. Osipov, “Differentsialno-raznostnaya igra sblizheniya s funktsionalnym tselevym mnozhestvom”, Prikl. matem. i mekh., 37:1 (1973), 3–13 | MR | Zbl

[11] N. N. Krasovskii, Yu. S. Osipov, “Zadacha upravleniya s nepolnoi informatsiei”, Izv. AN SSSR. Ser. mekh. tverd. tela, 1973, no. 4, 5–14 | MR

[12] N. N. Krasovskii, Yu. S. Osipov, “K teorii differentsialnykh igr s nepolnoi informatsiei”, Dokl. AN SSSR, 215:4 (1974), 780–783 | MR | Zbl

[13] Yu. S. Osipov, “An information game problem”, Optimization Techniques: IFIP Technical Conference (Novosibirsk, July 1–7, 1974), Lect. Notes Comput. Sci., 27, Springer, Berlin, 1975, 482–486 | Zbl

[14] Yu. S. Osipov, “K teorii differentsialnykh igr v sistemakh s raspredelennymi parametrami”, Dokl. AN SSSR, 223:6 (1975), 1314–1317 | MR | Zbl

[15] I. F. Vaisburd, Yu. S. Osipov, “Differentsialnaya igra sblizheniya dlya sistem s raspredelennymi parametrami”, Prikl. matem. i mekh., 39:5 (1975), 772–779 | MR | Zbl

[16] A. B. Kurzhanskii, Yu. S. Osipov, “Minimax control and estimation problems in systems with distributed parameters”, Proceedings of the IFAC 6th World Congress (Boston / Cambridge, MA, 1975), IFAC, Düsseldorf, 1975, 15.5/1–15.5/11 | MR

[17] Yu. S. Osipov, S. P. Okhezin, “K teorii differentsialnykh igr v parabolicheskikh sistemakh”, Dokl. AN SSSR, 226:6 (1976), 1267–1270 | MR | Zbl

[18] L. P. Alesenko, Yu. S. Osipov, “O regulyarizatsii upravlenii v differentsialno-raznostnoi igre sblizheniya-ukloneniya”, Differents. uravneniya, 12:6 (1976), 999–1006 | MR | Zbl

[19] Yu. S. Osipov, “Pozitsionnoe upravlenie v parabolicheskikh sistemakh”, Prikl. matem. i mekh., 41:2 (1977), 195–201 | MR | Zbl

[20] Yu. S. Osipov, S. P. Okhezin, “K teorii pozitsionnogo upravleniya v giperbolicheskikh sistemakh”, Dokl. AN SSSR, 233:4 (1977), 551–554 | MR | Zbl

[21] A. I. Korotkii, Yu. S. Osipov, “Approksimatsiya v zadachakh pozitsionnogo upravleniya parabolicheskimi sistemami”, Prikl. matem. i mekh., 42:4 (1978), 599–605 | MR | Zbl

[22] Yu. S. Osipov, A. V. Kryazhimskii, S. P. Okhezin, “Zadachi upravleniya v sistemakh s raspredelennymi parametrami”, Dinamika upravlyaemykh sistem (Irkutsk, 1977), Nauka, Novosibirsk, 1979, 199–208 | MR

[23] A. I. Korotkii, Yu. S. Osipov, “O pozitsionnom upravlenii v sistemakh s raspredelennymi parametrami”, Prikl. matem. i mekh., 44:4 (1980), 611–617 | MR | Zbl

[24] Yu. S. Osipov, V. G. Pimenov, “O pozitsionnom upravlenii pri posledeistvii v upravlyayuschikh silakh”, Prikl. matem. i mekh., 45:2 (1981), 223–229 | MR | Zbl

[25] A. V. Kryazhimskii, Yu. S. Osipov, “Metod pozitsionnoi regulyarizatsii v zadache o postroenii dvizheniya”, Annotatsii dokladov 5-go Vsesoyuznogo s'ezda po teoreticheskoi i prikladnoi mekhanike, Izd-vo “Nauka” KazSSR, Alma-Ata, 1981, 214

[26] A. V. Kryazhimskii, Yu. S. Osipov, “O modelirovanii upravleniya v dinamicheskoi sisteme”, Izv. AN SSSR. Ser. tekhn. kibernetika, 1983, no. 2, 51–60 | MR | Zbl

[27] A. V. Kryazhimskii, V. I. Maksimov, Yu. S. Osipov, “O pozitsionnom modelirovanii v dinamicheskikh sistemakh”, Prikl. matem. i mekh., 47:6 (1983), 883–890 | MR | Zbl

[28] Yu. S. Osipov, A. V. Kryazhimskii, “O modelirovanii parametrov dinamicheskoi sistemy”, Zadachi upravleniya i modelirovaniya v dinamicheskikh sistemakh, UNTs AN SSSR, Sverdlovsk, 1984, 47–68 | MR

[29] A. V. Krjazimskii, Yu. S. Osipov, “On positional calculation of $\Omega$-normal controls in dynamical systems”, Problems Control Inform. Theory, 13:6 (1984), 425–436 | MR | Zbl

[30] Yu. S. Osipov, A. V. Krjazimskii, “Positional modeling of stochastic control in dynamical systems”, Stochastic optimization (Kiev, 1984), Lecture Notes in Control and Inform. Sci., 81, Springer, Berlin, 1986, 696–704 | MR | Zbl

[31] Yu. S. Osipov, A. V. Kryazhimskii, “Metod funktsii Lyapunova v zadache modelirovaniya dvizheniya”, Ustoichivost dvizheniya, Nauka, Novosibirsk, 1985, 53–56

[32] A. V. Kryazhimskii, Yu. S. Osipov, “Metod funktsii Lyapunova v zadache o modelirovanii dvizhenii”, Annotatsii dokladov IV Chetaevskoi konferentsii po ustoichivosti dvizheniya, analiticheskoi mekhanike i upravleniyu dvizheniem (Zvenigorod, 1985), 35

[33] Yu. S. Osipov, “Zadachi dinamicheskogo vosstanovleniya”, Chislo i mysl, 10, Znanie, M., 1987, 7–27 | MR

[34] A. V. Kryazhimskii, Yu. S. Osipov, “Obratnye zadachi dinamiki i upravlyaemye modeli”, Mekhanika i nauchno-tekhnicheskii progress. T. 1: Obschaya i prikladnaya mekhanika, Nauka, M., 1987, 196–211 | MR

[35] A. V. Kryazhimskii, Yu. S. Osipov, “Ustoichivye resheniya obratnykh zadach dinamiki upravlyaemykh sistem”, Optimalnoe upravlenie i differentsialnye igry, Tr. MIAN, 185, ed. L. S. Pontryagin, Nauka, M., 1988, 126–146 | MR | Zbl

[36] A. V. Kryazhimskii, Yu. S. Osipov, “O metodakh pozitsionnogo modelirovaniya upravleniya v dinamicheskikh sistemakh”, Kachestvennye voprosy teorii differentsialnykh uravnenii i upravlyaemykh sistem, Sverdlovsk, 1988, 34–44 | MR | Zbl

[37] A. V. Kryazhimskii, Yu. S. Osipov, “Ob ustoichivom pozitsionnom vosstanovlenii upravleniya po izmereniyam chasti koordinat”, Nekotorye zadachi upravleniya i ustoichivosti, UNTs AN SSSR, Sverdlovsk, 1989, 33–47 | MR | Zbl

[38] Yu. S. Osipov, A. V. Kryazhimskii, Inverse problem for ordinary differential equations: dynamical solutions, Gordon Breach, Basel, 1995 | MR | Zbl

[39] Yu. S. Osipov, A. V. Kryazhimskii, “O dinamicheskom reshenii operatornykh uravnenii”, Dokl. AN SSSR, 269:3 (1983), 552–556 | MR | Zbl

[40] A. V. Kryazhimskii, Yu. S. Osipov, “O dinamicheskoi regulyarizatsii lineinykh algebraicheskikh uravnenii”, Zadachi pozitsionnogo modelirovaniya, UNTs AN SSSR, Sverdlovsk, 1986, 41–84 | Zbl

[41] A. V. Kryazhimskii, Yu. S. Osipov, “O nailuchshem priblizhenii operatora differentsirovaniya v klasse neuprezhdayuschikh operatorov”, Matem. zametki, 37:2 (1985), 192–199 | MR | Zbl

[42] A. V. Kryazhimskii, Yu. S. Osipov, “K regulyarizatsii vypukloi ekstremalnoi zadachi s netochno zadannymi ogranicheniyami. Prilozhenie k zadache optimalnogo upravleniya s fazovymi ogranicheniyami”, Nekotorye metody pozitsionnogo i programmnogo upravleniya, UNTs AN SSSR, Sverdlovsk, 1987, 34–54 | MR

[43] A. V. Kryazhimskii, Yu. S. Osipov, “Ekstremalnye zadachi s otdelimymi grafikami”, Kibernetika i sistemn. analiz, 2002, no. 2, 32–55 | MR | Zbl

[44] A. V. Kryazhimskii, Yu. S. Osipov, “Metod ekstremalnogo sdviga i zadachi optimizatsii”, Trudy IMM UrO RAN, 10:2 (2004), 83–105 | MR | Zbl

[45] A. V. Kim, A. I. Korotkii, Yu. S. Osipov, “Obratnye zadachi dinamiki parabolicheskikh sistem”, Prikl. matem. i mekh., 54:5 (1990), 754–759 | MR | Zbl

[46] Yu. S. Osipov, Inverse problems of dynamics for systems described by parabolic inequality, Working paper WP-89-101, International Institute for Applied Systems Analysis, Laxenburg, 1989

[47] Yu. S. Korbich, V. I. Maksimov, Yu. S. Osipov, “Dinamicheskoe modelirovanie upravlenii v nekotorykh parabolicheskikh sistemakh”, Prikl. matem. i mekh., 54:3 (1990), 355–360 | MR | Zbl

[48] A. I. Korotkii, Yu. S. Osipov, “Dinamicheskoe modelirovanie parametrov v giperbolicheskikh sistemakh”, Izv. AN SSSR. Ser. tekhn. kibernetika, 1991, no. 2, 154–164 | MR | Zbl

[49] A. V. Kryazhimskii, V. I. Maksimov, Yu. S. Osipov, Zadachi dinamicheskoi regulyarizatsii dlya sistem s raspredelennymi parametrami, Preprint, IMM UrO AN SSSR, Sverdlovsk, 1991

[50] Yu. S. Osipov, “Inverse problem of dynamics for systems described by parabolic inequality”, Modelling and inverse problems of control for distributed parameter systems (Laxenburg, 1989), Lecture Notes in Control and Inform. Sci., 154, Springer, Berlin, 1991, 127–134 | MR | Zbl

[51] Yu. S. Osipov, A. I. Korotkii, “On dynamical restoration of parameters of elliptic systems”, Ill-posed problems in natural sciences (Moscow, 1991), VSP, Utrecht, 1992, 108–117 | MR | Zbl

[52] Yu. S. Osipov, On the reconstruction of a parameter for a hyperbolic systems, Working paper WP-91-54, International Institute for Applied Systems Analysis, Laxenburg, 1991

[53] Yu. S. Osipov, “On reconstruction of coefficients for differential equations”, Current problems of analysis and mathematical physics (Taormina, 1992), Univ. Roma “La Sapienza”, Rome, 1993, 195–199 | MR | Zbl

[54] Yu. S. Osipov, A. V. Kryazhimskii, V. I. Maksimov, “Dynamical inverse problems for systems with distributed parameters”, J. Inverse Ill-Posed Probl., 4:4 (1996), 267–282 | MR | Zbl

[55] A. V. Kryazhimskii, V. I. Maksimov, Yu. S. Osipov, Reconstruction of boundary sources through sensor observations, Working paper WP-96-97, International Institute for Applied Systems Analysis, Laxenburg, 1996

[56] A. V. Kryazhimskii, V. I. Maksimov, Yu. S. Osipov, “O rekonstruktsii ekstremalnykh vozmuschenii v parabolicheskikh uravneniyakh”, ZhVM i MF, 37:3 (1997), 291–301 | MR | Zbl

[57] Yu. S. Osipov, A. V. Kryazhimskii, V. I. Maksimov, “Dinamicheskie obratnye zadachi dlya parabolicheskikh sistem”, Differents. uravneniya, 36:5 (2000), 579–597 | MR | Zbl

[58] Yu. S. Osipov, L.Pandolfi, V. I. Maksimov, “Zadacha robastnogo granichnogo upravleniya: sluchai kraevykh uslovii Dirikhle”, Dokl. RAN, 374:3 (2000), 310–312 | MR | Zbl

[59] V. I. Maksimov, Yu. S. Osipov, L. Pandolfi, “Problems of dynamical reconstruction and robust boundary control: the case of Dirichlet boundary conditions”, Raspredelennye sistemy: optimizatsiya i prilozheniya v ekonomike i naukakh ob okruzhayuschei srede, IMM UrO RAN, Ekaterinburg, 2000, 42–45 | MR

[60] Yu. S. Osipov, L. Pandolfi, V. I. Maksimov, “Problems of dynamical reconstruction and robust boundary control: the case of Dirichlet boundary conditions”, Distributed systems: optimization and economic-environmental applications (Ekaterinburg, 2000), J. Inverse Ill-Posed Probl., 9:2 (2001), 149–162 | MR | Zbl

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

[62] Yu. S. Osipov, A. P. Suetov, “Ob odnoi zadache Zh.-L. Lionsa”, Dokl. AN SSSR, 276:2 (1984), 288–291 | MR | Zbl

[63] Yu. S. Osipov, A. P. Suetov, “Kachestvennye voprosy teorii optimizatsii konstruktsii”, Voprosy kachestvennoi teorii differentsialnykh uravnenii, Nauka, Novosibirsk, 1988, 237–244 | MR

[64] Yu. S. Osipov, A. P. Suetov, Suschestvovanie optimalnykh form ellipticheskikh sistem. Sluchai kraevykh uslovii Dirikhle, IMM UrO AN SSSR, Sverdlovsk, 1990

[65] A. V. Kryazhimskii, Yu. S. Osipov, “O differentsialno-evolyutsionnykh igrakh”, Optimalnoe upravlenie i differentsialnye uravneniya, K 70-letiyu so dnya rozhdeniya akademika E. F. Mischenko, Tr. MIAN, 211, ed. R. V. Gamkrelidze, Nauka, M., 1995, 257–287 | MR | Zbl

[66] A. V. Kryazhimskii, Yu. S. Osipov, “Approksimatsionnaya lineinaya reduktsiya v differentsialnoi igre navedeniya-ukloneniya”, Optimalnoe upravlenie, differentsialnye uravneniya i gladkaya optimizatsiya, K 70-letiyu so dnya rozhdeniya chlena-korrespondenta RAN R. V. Gamkrelidze, Tr. MIAN, 220, Nauka, M., 1998, 173–194 | MR | Zbl

[67] A. V. Kryazhimskii, Yu. S. Osipov, “O dvumernoi reduktsii v differentsialnoi igre kachestva”, Algebra. Topologiya. Differentsialnye uravneniya i ikh prilozheniya, K 90-letiyu so dnya rozhdeniya akademika L. S. Pontryagina, Tr. MIAN, 224, Nauka, M., 1999, 218–233 | MR | Zbl

[68] Yu. S. Osipov, “Pakety programm: podkhod k resheniyu zadach pozitsionnogo upravleniya s nepolnoi informatsiei”, UMN, 61:4 (2006), 25–76 | MR | Zbl