Geodesic
Constructing open-loop and closed-loop solutions of linear-quadratic optimal control problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 10, pp. 1748-1779 Cet article a éte moissonné depuis la source Math-Net.Ru

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A linear-quadratic optimal control problem subject to geometric constraints on the controls is studied. Techniques for finding the optimal open-loop control and constructing a closed-loop control are described. The problem solution can include special intervals and sections with chattering modes. The proposed techniques make it possible to find special intervals and construct realizable approximations of unrealizable chattering modes to any degree of accuracy. 
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     title = {Constructing open-loop and closed-loop solutions of linear-quadratic optimal control problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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R. Gabasov; F. M. Kirillova; N. S. Pavlenok. Constructing open-loop and closed-loop solutions of linear-quadratic optimal control problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 10, pp. 1748-1779. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_10_a1/

[1] Bliss G. A., Lektsii po variatsionnomu ischisleniyu, Izd-vo inostr. lit., M., 1950

[2] Feldbaum A. A., Osnovy teorii optimalnykh avtomaticheskikh sistem, Fizmatgiz, M., 1963 | MR

[3] Braison A., Yu-Shi Kho, Prikladnaya teoriya optimalnogo upravleniya. Optimizatsiya, otsenka i upravlenie, Mir, M., 1972

[4] Letov A. M., “Analiticheskoe konstruirovanie regulyatorov. I”, Avtomatika i telemekhan., 21:4 (1960), 661–665

[5] Kalman R., “Ob obschei teoriii sistem upravleniya”, Tr. I Mezhdunar. kongressa Mezhdunar. federatsii po avtomatich. upravleniyu (IFAK), v. 1, Izd-vo AN SSSR, M., 1961, 521–547

[6] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E..F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1983 | MR | Zbl

[7] Gabasov R., Kirillova F. M., Osobye optimalnye upravleniya, Fizmatlit, M., 1973 | MR

[8] Fuller A. T., “Optimizatsiya releinykh sistem regulirovaniya po razlichnym kriteriyam kachestva”, Teoriya diskretnykh, optimalnykh i samonastraivayuschikhsya sistem, Tr. I Mezhdunar. kongressa Mezhdunar. federatsii po avtomatich. upravleniyu (IFAK), Izd-vo AN SSSR, M., 1961, 584–605

[9] Srochko V. A., Iteratsionnye metody resheniya zadach optimalnogo upravleniya, Fizmatlit, M., 2000

[10] Kyuntsi G. P., Krelle V., Nelineinoe programmirovanie, Sov. radio, M., 1965

[11] Balashevich N. V., Gabasov R., Kirillova F. M., “Chislennye metody programmnoi i pozitsionnoi optimizatsii lineinykh sistem upravleniya”, Zh. vychisl. matem. i matem. fiz., 40:6 (2000), 838–859 | MR | Zbl

[12] Gabasov R., Kirillova F. M., Tyatyushkin A. I., Konstruktivnye metody optimizatsii. Ch. 1. Lineinye zadachi, Universitetskoe, Minsk, 1984 | MR

[13] Balashevich N. V., Gabasov R., Kirillova F. M., “Algoritmy programmnoi i pozitsionnoi optimizatsii lineinykh sistem upravleniya s promezhutochnymi fazovymi ogranicheniyami”, Zh. vychisl. matem. i matem. fiz., 41:10 (2001), 1485–1504 | MR | Zbl

[14] Gabasov R., Kirillova F. M., Konstruktivnye metody optimizatsii. Ch. 2. Zadachi upravleniya, Universitetskoe, Minsk, 1984 | MR

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