Geodesic
Controllability and synthesis of control for nonlinear systems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2009), pp. 3-13 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The problems of controllability of motion with feedback are solved when the equations of a system have linear approximation, at that by virtue the smallness of the nonlinear part and controllability of the linear approximation this property is preserved at the nonlinear perturbation. The problem is solved by Lyapunov functions method and comparison methods for a finite and infinite time. The results are illustrated on the example of the controllability for the simplest mechanical system.
Keywords: nonlinear systems, ordinary differential equations, controllability, Lyapunov functions, comparison methods. 
@article{IVM_2009_10_a0,
     author = {E. V. Voskresenskii},
     title = {Controllability and synthesis of control for nonlinear systems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--13},
     year = {2009},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_10_a0/}
}
TY  - JOUR
AU  - E. V. Voskresenskii
TI  - Controllability and synthesis of control for nonlinear systems
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2009
SP  - 3
EP  - 13
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/IVM_2009_10_a0/
LA  - ru
ID  - IVM_2009_10_a0
ER  - 
%0 Journal Article
%A E. V. Voskresenskii
%T Controllability and synthesis of control for nonlinear systems
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2009
%P 3-13
%N 10
%U http://geodesic.mathdoc.fr/item/IVM_2009_10_a0/
%G ru
%F IVM_2009_10_a0
E. V. Voskresenskii. Controllability and synthesis of control for nonlinear systems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2009), pp. 3-13. http://geodesic.mathdoc.fr/item/IVM_2009_10_a0/

[1] Voskresenskii E. V., Metody sravneniya v nelineinom analize, Izd-vo Saransk. un-ta, Saransk, 1990, 224 pp. | MR

[2] Bylov B. F., Vinograd R. E., Grobman D. M., Nemytskii V. V., Teoriya pokazatelei Lyapunova i ee prilozheniya k voprosam ustoichivosti, Nauka, M., 1966, 576 pp. | MR | Zbl

[3] Voskresenskii E. V., Asimptoticheskie metody: teoriya i prilozheniya, SVMO, Saransk, 2000, 300 pp.

[4] Zubov V. I., Lektsii po teorii upravleniya, Nauka, M., 1975, 496 pp. | MR | Zbl

[5] Ananevskii I. M., “Sintez upravleniya lineinymi sistemami s pomoschyu metodov teorii ustoichivosti dvizheniya”, Differents. uravneniya, 39:1 (2003), 3–11 | MR

[6] Rush N., Abets P., Lalua M., Pryamoi metod Lyapunova v teorii ustoichivosti, Mir, M., 1980, 300 pp. | MR

[7] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1983, 392 pp. | MR | Zbl