Geodesic
Asymptotic behavior of the solution of a singularly perturbed linear-quadratic terminal control problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 3, pp. 423-433 
A. I. Kalinin. Asymptotic behavior of the solution of a singularly perturbed linear-quadratic terminal control problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 3, pp. 423-433. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_3_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A quadratic terminal cost functional is minimized on the trajectories of a linear singularly perturbed system. Equality constraints are imposed on the right end of the trajectories, while the multidimensional controls are bounded in the Euclidean norm. An algorithm is proposed for constructing asymptotic approximations to the solution of the problem.

[1] Vasileva A. B., Dmitriev M. G., “Singulyarnye vozmuscheniya v zadachakh optimalnogo upravleniya”, Itogi nauki i tekhn. Ser. Matem. anal., 20, VINITI, M., 1982, 3–77 | MR

[2] Kokotovic P. V., Khalil H. K., Singular perturbations in systems and control, Macmillan, N. Y., 1986 | MR

[3] Kalinin A. I., “Asimptotika reshenii vozmuschennykh zadach optimalnogo upravleniya”, Izv. RAN. Tekhn. kibernetika, 1994, no. 3, 104–114 | MR | Zbl

[4] Dmitriev M. G., Kurina G. A., “Singulyarnye vozmuscheniya v zadachakh upravleniya”, Avtomatika i telemekhan., 2006, no. 1, 3–51 | MR | Zbl

[5] Rakitskii Yu. V., Ustinov S. M., Chernorutskii N. G., Chislennye metody resheniya zhestkikh sistem, Nauka, M., 1979 | MR

[6] Grudo Ya. O., Kalinin A. I., “Asimptoticheskaya optimizatsiya nelineinykh singulyarno vozmuschennykh sistem pri ogranichenii upravleniya gipersferoi”, Differents. ur-niya, 44:11 (2008), 1472–1481 | MR | Zbl

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

[8] Vasileva A. B., Butuzov V. F., Asimptoticheskie razlozheniya reshenii singulyarno vozmuschennykh uravnenii, Nauka, M., 1973 | MR

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

[10] Gabasov R., Kirillova F. M., Osobye optimalnye upravleniya, Nauka, M., 1973 | MR