Geodesic
To solution of control problems of nonlinear systems on a finite time interval
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 46 (2015) no. 2, pp. 202-215.

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

A nonlinear controlled system on a finite time interval is under consideration. The problem of rapprochement to a target set in the phase space in this period of time is studied. The scheme of approximate calculation of solvability sets based on the use of retrograde step by step procedures is proposed.
Keywords: control system, movement, reachability set, integral funnel, control, solvability set.
Mots-clés : problem of rapprochement 
@article{IIMI_2015_46_2_a25,
     author = {V. N. Ushakov and A. R. Matviychuk},
     title = {To solution of control problems of nonlinear systems on a finite time interval},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {202--215},
     publisher = {mathdoc},
     volume = {46},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a25/}
}
TY  - JOUR
AU  - V. N. Ushakov
AU  - A. R. Matviychuk
TI  - To solution of control problems of nonlinear systems on a finite time interval
JO  - Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
PY  - 2015
SP  - 202
EP  - 215
VL  - 46
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a25/
LA  - ru
ID  - IIMI_2015_46_2_a25
ER  - 
%0 Journal Article
%A V. N. Ushakov
%A A. R. Matviychuk
%T To solution of control problems of nonlinear systems on a finite time interval
%J Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
%D 2015
%P 202-215
%V 46
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a25/
%G ru
%F IIMI_2015_46_2_a25
V. N. Ushakov; A. R. Matviychuk. To solution of control problems of nonlinear systems on a finite time interval. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 46 (2015) no. 2, pp. 202-215. http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a25/

[1] Krasovskii N. N., Control of dynamic system, Nauka, M., 1985, 520 pp.

[2] Kurzhanskii A. B., “An analytical description of the beam of enduring trajectories of a differential system”, Dokl. AN SSSR, 287:5 (1986), 1047–1050 (in Russian) | MR | Zbl

[3] Kryazhimskii A. V., Osipov Yu. S., “Differential-difference game of encounter with a functional target set”, J. Appl. Math. Mech., 37:1 (1973), 1–10 | DOI | MR | Zbl

[4] Kurzhanskii A. B., Selected works, Moscow State University, M., 2009, 756 pp.

[5] Krasovskii N. N., Subbotin A. I., Positional differential games, Nauka, M., 1974, 456 pp.

[6] Chernous'ko F. L., Evaluation of the phase state of dynamical systems: the ellipsoid method, Nauka, M., 1988, 319 pp.

[7] Tonkov E. L., Panasenko E. A., “Invariant and stably invariant sets for differential inclusions”, Proceedings of the Steklov Institute of Mathematics, 262 (2008), 194–212 | DOI | MR | MR | Zbl

[8] Guseinov Kh. G., Moiseev A. N., Ushakov V. N., “The approximation of reachable domains of control systems”, J. Appl. Math. Mech., 62:2 (1998), 169–175 | DOI | MR | Zbl

[9] Gusev M. I., “Estimates of reachable sets of multidimensional control systems with nonlinear interconnections”, Proceedings of the Steklov Institute of Mathematics, 269, 2010, 134–146 | DOI | Zbl

[10] Filippova T. F., “Construction of set-valued estimates of reachable sets for some nonlinear dynamical systems with impulsive control”, Proceedings of the Steklov Institute of Mathematics, 269, 2010, 95–102 DOI: 10.1134/S008154381006009X | DOI | Zbl

[11] Ushakov V. N., Matviichuk A. R., Parshikov G. V., “A method for constructing a resolving control in an approach problem based on attraction to the feasibility set”, Proceedings of the Steklov Institute of Mathematics, 284, no. suppl. 1, 2014, 135–144 DOI: 10.1134/S0081543814020126 | DOI | MR

[12] Ushakov A. V., “On one version of approximate permitting control calculation in a problem of approaching”, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2012, no. 4, 94–107

[13] Panasyuk A. I., “Equations of the dynamics of sets of reachability in problems of optimization and control under conditions of uncertainty”, J. Appl. Math. Mech., 50:4 (1986), 405–415 | DOI | MR | Zbl

[14] Blagodatskikh V. I., Filippov A. F., “Differential inclusions and optimal control”, Proceedings of the Steklov Institute of Mathematics, 169 (1986), 199–259 | MR | Zbl | Zbl

[15] Taras'ev A. M., Ushakov V. N., Khripunov A. P., “On a computational algorithm for solving game control problems”, J. Appl. Math. Mech., 51:2 (1987), 167–172 | DOI | MR | Zbl