Mathematical model of control of stochastical object with distributed parameters
Matematičeskoe modelirovanie, Tome 21 (2009) no. 2, pp. 85-102.

Voir la notice de l'article provenant de la source Math-Net.Ru

The partial differential equation for describing optimum movement of nonmarkov system with distributed parameters under random influences with arbitrary distribution is derived. Decision of equation by means of interpolation Kantorovich's method in basis of Lagrange functions of influence is realized. Algorithm of output of optimum control at base of principle of sequence approach is created. By using numerical examination is established, that the method ensures high accuracy of solution.
@article{MM_2009_21_2_a8,
     author = {A. N. Kudinov and A. N. Katulev and M. F. Malevinsky},
     title = {Mathematical model of control of stochastical object with distributed parameters},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {85--102},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2009_21_2_a8/}
}
TY  - JOUR
AU  - A. N. Kudinov
AU  - A. N. Katulev
AU  - M. F. Malevinsky
TI  - Mathematical model of control of stochastical object with distributed parameters
JO  - Matematičeskoe modelirovanie
PY  - 2009
SP  - 85
EP  - 102
VL  - 21
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2009_21_2_a8/
LA  - ru
ID  - MM_2009_21_2_a8
ER  - 
%0 Journal Article
%A A. N. Kudinov
%A A. N. Katulev
%A M. F. Malevinsky
%T Mathematical model of control of stochastical object with distributed parameters
%J Matematičeskoe modelirovanie
%D 2009
%P 85-102
%V 21
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2009_21_2_a8/
%G ru
%F MM_2009_21_2_a8
A. N. Kudinov; A. N. Katulev; M. F. Malevinsky. Mathematical model of control of stochastical object with distributed parameters. Matematičeskoe modelirovanie, Tome 21 (2009) no. 2, pp. 85-102. http://geodesic.mathdoc.fr/item/MM_2009_21_2_a8/

[1] Kudinov A. N., Katulev A. N., Malevinskii M. F., Matematicheskie metody otsenki pokazatelei bezopasnosti sostoyaniya dinamicheskikh sistem, Izd. MGU im. M. V. Lomonosova, M., 2005

[2] Kurzhanskii A. B., “O zadachakh sinteza upravlenii po realno dostupnoi informatsii”, Vestnik Moskovskogo universiteta. Ser. 15. Vychislitelnaya matematika i kibernetika, spetsvypusk (2005), 122–133

[3] Pupkov K. A., Egupov N. D., Makarenkov A. M., Trofimov A. I., Teoriya i kompyuternye metody issledovaniya stokhasticheskikh sistem, Fizmatlit, M., 2003, 400 pp.

[4] Klyatskin V. I., Dinamika stokhasticheskikh sistem, Fizmatlit, M., 2003

[5] Bellman R., Dinamicheskoe programmirovanie, IIL, M., 1960 | MR

[6] Khovard R. A., Dinamicheskoe programmirovanie i markovskie protsessy, Sov. radio, M., 1964 | MR

[7] Prokhorov Yu. V., Rozanov Yu. A., Teoriya veroyatnostei. Osnovnye ponyatiya, predelnye teoremy. Sluchainye protsessy, Nauka, M., 1967 | MR | Zbl

[8] Paraev Yu. I., Vvedenie v statisticheskuyu dinamiku protsessov upravleniya i filtratsii, Sov. radio, M., 1976

[9] Khazen E. M., Metody optimalnykh statisticheskikh reshenii i zadachi optimalnogo upravleniya, Sov. radio, M., 1968 | Zbl

[10] Evlanov L. G., Konstantinov V. M., Sistemy so sluchainymi parametrami, M., Nauka | MR

[11] Krylov N. V., Upravlyaemye protsessy diffuzionnogo tipa, Nauka, M., 1977 | MR

[12] Gikhman I. I., Skorokhod A. V., Vvedenie v teoriyu sluchainykh protsessov, Nauka, M., 1977 | MR

[13] Andreeva E. A., Kolmanovskii V. B., Shaikhet L. E., Upravlenie sistemami s posledeistviem, Nauka, M., 1991 | MR

[14] Yarlykov M. S., Mironov M. A., Markovskaya teoriya otsenivaniya sluchainykh protsessov, Radio i svyaz, M., 1993 | MR | Zbl

[15] Krasovskii A. A., Bukov V. N., Shendrik V. S., Universalnye algoritmy optimalnogo upravleniya nepreryvnymi protsessami, Nauka, M., 1977 | MR

[16] Pugachev V. N., Lifshits N. A., Veroyatnostnyi analiz sistem avtomaticheskogo upravleniya, Sov. radio, M., 1963 | Zbl

[17] Kazakov E. I., Dostupov B. G., Statisticheskaya dinamika nelineinykh avtomaticheskikh sistem, FML, M., 1961

[18] Gurli S. A., Sou V. Kh., Vu Dzh., “Nelokalnye uravneniya reaktsii diffuzii s zapazdyvaniem. Biologicheskie modeli i nelineinaya dinamika”, Trudy mezhdunarodnoi konferentsii po differentsialnym i funktsionalno-differentsialnym uravneniyam – satellita Mezhdunarodnogo kongressa matematikov ICM-2002, Chast 1 (Moskva, MAI, 11–17 avgusta, 2002), Sovremennaya matematika. Fundamentalnye napravleniya, 1, MAI, M., 2003, 84–120 | MR | Zbl

[19] Moiseev N. N., Chislennye metody v teorii optimalnykh sistem, Nauka, M., 1971 | MR

[20] Ishmukhametov A. Z., Voprosy ustoichivosti i approksimatsii zadach optimalnogo upravleniya sistemami s raspredelennymi parametrami, VTs RAN, M., 2001

[21] Kuznetsov D. F., Chislennoe modelirovanie stokhasticheskikh differentsialnykh uravnenii i stokhasticheskikh integralov, SPbGTU, SPb., 2001

[22] Riznichenko G. Yu., Rubin A. B., Matematicheskie modeli biologicheskikh produktsionnykh protsessov, Izd. MGU im. M. V. Lomonosova, M., 1993

[23] Matematicheskaya entsiklopediya, T. 2, Izd. “Sovetskaya entsiklopediya”, M., 1979

[24] Kudinov A. N., Katulev A. N., Malevinskii M. F., “Vosstanovlenie signala obobschennym ryadom Kotelnikova”, Izvestiya VUZov. Radiofizika (Nizhnii Novgorod), 49:8 (2006), 712–717

[25] Chernetskii V. I., Analiz tochnosti nelineinykh sistem upravleniya, Mashinostroenie, M., 1968

[26] Tikhonov V. I., Mironov M. A., Markovskie protsessy, Sov. radio, M., 1977 | MR | Zbl

[27] Moiseev N. N., Ivanilov Yu. M., Stolyarova E. M., Metody optimizatsii, Nauka, M., 1978

[28] Bakhvalov N. S., Zhidkov N. P., Kobelkov G. M., Chislennye metody, Nauka, M., 1987 | MR | Zbl

[29] Fedorenko R. P., Priblizhennoe reshenie zadach optimalnogo upravleniya, Nauka, M., 1978 | MR | Zbl

[30] Vorobev L. M, Vorobeva T. M., Nelineinye preobrazovaniya v prikladnykh variatsionnykh zadachakh, Energiya, M., 1972