Optimal Synthesis in a~Control Problem with Lipschitz Input Data
Informatics and Automation, Optimal control, Tome 262 (2008), pp. 240-252.

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

We propose a numerical algorithm for constructing an optimal synthesis in the control problem for a nonlinear system on a fixed time interval. We estimate the difference between the values of the cost functional on optimal trajectories and on the trajectories constructed according to this algorithm. The operation of the algorithm is illustrated by solving model examples on the plane.
@article{TRSPY_2008_262_a17,
     author = {N. N. Subbotina and T. B. Tokmantsev},
     title = {Optimal {Synthesis} in {a~Control} {Problem} with {Lipschitz} {Input} {Data}},
     journal = {Informatics and Automation},
     pages = {240--252},
     publisher = {mathdoc},
     volume = {262},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2008_262_a17/}
}
TY  - JOUR
AU  - N. N. Subbotina
AU  - T. B. Tokmantsev
TI  - Optimal Synthesis in a~Control Problem with Lipschitz Input Data
JO  - Informatics and Automation
PY  - 2008
SP  - 240
EP  - 252
VL  - 262
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2008_262_a17/
LA  - ru
ID  - TRSPY_2008_262_a17
ER  - 
%0 Journal Article
%A N. N. Subbotina
%A T. B. Tokmantsev
%T Optimal Synthesis in a~Control Problem with Lipschitz Input Data
%J Informatics and Automation
%D 2008
%P 240-252
%V 262
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2008_262_a17/
%G ru
%F TRSPY_2008_262_a17
N. N. Subbotina; T. B. Tokmantsev. Optimal Synthesis in a~Control Problem with Lipschitz Input Data. Informatics and Automation, Optimal control, Tome 262 (2008), pp. 240-252. http://geodesic.mathdoc.fr/item/TRSPY_2008_262_a17/

[1] Aizeks R., Differentsialnye igry, Mir, M., 1967 | MR

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

[3] Blagodatskikh V. I., “Printsip maksimuma dlya differentsialnykh vklyuchenii”, Tr. MIAN, 166, Nauka, M., 1984, 23–43 | MR | Zbl

[4] Boltyanskii V. G., Matematicheskie metody optimalnogo upravleniya, Nauka, M., 1966 | MR

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

[6] Kamzolkin D. V., “Chislennyi metod priblizhennogo vychisleniya funktsii tseny dlya zadachi optimalnogo upravleniya s terminalnym funktsionalom”, Vychislitelnye metody i programmirovanie, 5:2 (2004), 240–251

[7] Klark F., Optimizatsiya i negladkii analiz, Nauka, M., 1988 | MR | Zbl

[8] Krasovskii N. N., Teoriya upravleniya dvizheniem: Lineinye sistemy, Nauka, M., 1968 | MR

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

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

[11] Subbotina N. N., Metod kharakteristik dlya uravnenii Gamiltona–Yakobi i ego prilozheniya v dinamicheskoi optimizatsii, Sovr. matematika i ee pril., 20, In-t kibernetiki AN Gruzii, Tbilisi, 2004

[12] Subbotina N. N., “Obobschennyi metod kharakteristik v zadache optimalnogo upravleniya s lipshitsevymi vkhodnymi dannymi”, Izv. UrGU. Matematika i mekhanika, 2006, no. 4, 177–186 | Zbl

[13] Subbotina N. N., Tokmantsev T. B., “Algoritm postroeniya minimaksnogo resheniya uravneniya Bellmana v zadache Koshi s dopolnitelnymi ogranicheniyami”, Tr. In-ta matematiki i mekhaniki UrO RAN, 12:1 (2006), 208–215 | MR

[14] Subbotina N. N., Tokmantsev T. B., “Chislennaya approksimatsiya minimaksnogo resheniya uravneniya Bellmana v zadache Koshi s dopolnitelnymi ogranicheniyami”, Problemy teoreticheskoi i prikladnoi matematiki, Tr. 37-i reg. molodezh. konf., UrO RAN, Ekaterinburg, 2006, 357–361

[15] Subbotina N. N., Tokmantsev T. B., “Optimalnyi sintez v zadache upravleniya s lipshitsevymi vkhodnymi dannymi”, Matematicheskaya teoriya optimalnogo upravleniya i teoriya differentsialnykh vklyuchenii, Programma i annot. dokl. nauch. sem., MIRAN, M., 2006, 38–39

[16] Ushakov V. N., Khripunov A. P., “O priblizhennom postroenii reshenii v igrovykh zadachakh upravleniya”, PMM, 61:3 (1997), 413–421 | MR | Zbl

[17] Subbotin A. I., Generalized solutions of first-order PDEs: The dynamical optimization perspective, Birkhäuser, Boston, 1995 | MR