Geodesic
Adjoint variables to optimal control problems
Trudy Instituta matematiki i mehaniki, Mathematical control theory, differential games, Tome 10 (2004) no. 2, pp. 131-141 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

@article{TIMM_2004_10_2_a8,
     author = {N. N. Subbotina},
     title = {Adjoint variables to optimal control problems},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {131--141},
     year = {2004},
     volume = {10},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2004_10_2_a8/}
}
TY  - JOUR
AU  - N. N. Subbotina
TI  - Adjoint variables to optimal control problems
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2004
SP  - 131
EP  - 141
VL  - 10
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TIMM_2004_10_2_a8/
LA  - ru
ID  - TIMM_2004_10_2_a8
ER  - 
%0 Journal Article
%A N. N. Subbotina
%T Adjoint variables to optimal control problems
%J Trudy Instituta matematiki i mehaniki
%D 2004
%P 131-141
%V 10
%N 2
%U http://geodesic.mathdoc.fr/item/TIMM_2004_10_2_a8/
%G ru
%F TIMM_2004_10_2_a8
N. N. Subbotina. Adjoint variables to optimal control problems. Trudy Instituta matematiki i mehaniki, Mathematical control theory, differential games, Tome 10 (2004) no. 2, pp. 131-141. http://geodesic.mathdoc.fr/item/TIMM_2004_10_2_a8/

[1] Bellman R., Dinamicheskoe programmirovanie, Izd-vo inostr. lit., M., 1960, 400 pp. | MR

[2] Varga Dzh., Optimalnoe upravlenie differentsialnymi i funktsionalnymi uravneniyami, Nauka, M., 1977, 624 pp. | MR

[3] Gabasov R. F., Kirillova F. M., Kachestvennaya teoriya optimalnykh protsessov, Nauka, M., 1971, 508 pp. | MR

[4] Demyanov V. F., Malozemov V. N., Vvedenie v minimaks, Nauka, M., 1972, 363 pp. | MR

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

[6] Krasovskii N. N., Teoriya upravleniya dvizheniem, Nauka, M., 1968, 475 pp. | MR

[7] Krasovskii N. N., Upravlenie dinamicheskoi sistemoi, Nauka, M., 1985, 518 pp. | MR

[8] Leitman Dzh., Vvedenie v teoriyu optimalnogo upravleniya, Nauka, M., 1968, 202 pp. | Zbl

[9] Pontryagin L. S., Obyknovennye differentsialnye uravneniya, Nauka, M., 1965, 332 pp. | MR | Zbl

[10] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mischenko, Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1961, 392 pp. | MR | Zbl

[11] Rozonoer L. I., “Printsip maksimuma L. S. Pontryagina v teorii optimalnykh sistem. I”, Avtomatika i telemekhanika, 20:10 (1959), 1320–1334 | MR

[12] Stepanov V. V., Kurs differentsialnykh uravnenii, Fizmatgiz, M., 1959, 468 pp. | Zbl

[13] Subbotin A. I., Subbotina N. N., “Funktsiya optimalnogo rezultata v zadache upravleniya”, Dokl. AN SSSR, 266:2 (1982), 294–299 | MR | Zbl

[14] Subbotina N. N., “Neobkhodimye i dostatochnye usloviya optimalnosti upravlenii i traektorii”, Sintez optimalnogo upravleniya v igrovykh sistemakh, IMM UNTs AN SSSR, Sverdlovsk, 1986, 86–96 | MR

[15] Subbotina N. N., “Metod dinamicheskogo programmirovaniya dlya klassa lokalno-lipshitsevykh funktsii”, Dokl. RAN, 389:2 (2003), 169–172

[16] Bardi M., Capuzzo-Dolcetta I., Optimal Control and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations, Birkhäuser, Boston, 1997, 570 pp. | MR | Zbl

[17] Barron E. N., Jensen R., “The Pontryagin maximum principle from dynamic programming and viscosity solutions to first-order partial differential equations”, Trans. Amer. Math. Soc., 298:2 (1986), 635–641 | DOI | MR | Zbl

[18] Berkovitz L. D., “Optimal feedback controls”, SIAM J. Control Optimiz., 27 (1989), 991–1006 | DOI | MR | Zbl

[19] Cannarsa P., Frankowska H., “Some characterization of optimal trajectories in control theory”, SIAM J. Control Optimiz., 29 (1991), 1322–1347 | DOI | MR | Zbl

[20] F. H. Clarke, Yu. S. Ledyaev, R. J. Stern, P. R. Wolenski, Nonsmooth Analysis and Control Theory, Springer, New York, 1997, 278 pp. | MR

[21] Fleming W. H., Soner H. M., Controlled Markov Processes and Viscosity Solutions, Springer-Verlag, New York, 1993, 428 pp. | MR | Zbl

[22] Subbotin A. I., Generalized Solutions of First-Order PDEs: The Dynamical Optimization Perspective, Birkhäuser, Boston, 1995, 314 pp. | MR

[23] Zhou X.-Y., “Maximum principle, dynamic programming and their connection in deterministic controls”, J. Optim. Theory Appl., 65 (1990), 363–373 | DOI | MR | Zbl