Geodesic
On one piecewise constant control for nonlinear differential equations in Banach space
Matematičeskie trudy, Tome 27 (2024) no. 1, pp. 163-178 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The problem of controlling solutions to nonlinear differential equations is studied. equations with unstable equilibrium positions. It is assumed that the operator of the linearized problem is bounded and its spectrum is located inside the right half-plane. The existence of a control has been proven in which the solution can be maintained in any predetermined neighborhood of the equilibrium position for an arbitrarily long time. 
@article{MT_2024_27_1_a4,
     author = {A. A. Sedipkov},
     title = {On one piecewise constant control for nonlinear differential equations in {Banach} space},
     journal = {Matemati\v{c}eskie trudy},
     pages = {163--178},
     year = {2024},
     volume = {27},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2024_27_1_a4/}
}
TY  - JOUR
AU  - A. A. Sedipkov
TI  - On one piecewise constant control for nonlinear differential equations in Banach space
JO  - Matematičeskie trudy
PY  - 2024
SP  - 163
EP  - 178
VL  - 27
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MT_2024_27_1_a4/
LA  - ru
ID  - MT_2024_27_1_a4
ER  - 
%0 Journal Article
%A A. A. Sedipkov
%T On one piecewise constant control for nonlinear differential equations in Banach space
%J Matematičeskie trudy
%D 2024
%P 163-178
%V 27
%N 1
%U http://geodesic.mathdoc.fr/item/MT_2024_27_1_a4/
%G ru
%F MT_2024_27_1_a4
A. A. Sedipkov. On one piecewise constant control for nonlinear differential equations in Banach space. Matematičeskie trudy, Tome 27 (2024) no. 1, pp. 163-178. http://geodesic.mathdoc.fr/item/MT_2024_27_1_a4/

[1] R. E. Kalman, P. L. Falb, and M. A. Arbib., Topics in Mathematical System Theory, McGraw-Hill, New York, 1969 | MR | Zbl

[2] Fury M., Nistri P., Pera M. P., Zezza P. L., “Linear controllability by piecewise constant control with assigned switching times”, J. Optimize Theory and Apl., 45:2 (1985), 219-229 | DOI | MR

[3] Zezza P., “On reachable set for linear systems with piecewise constant controls”, Bol. Unione mat. Ital., 5:1 (1986), 127-137 | MR | Zbl

[4] Gryn L., “Discrete feedback stabilization of semilinear control systems”, Control, Optim. Calc. Var., 1 (1996), 207-224 | DOI | MR

[5] A. N. Kvitko, “On a control problem”, DIEQ, 40:6 (2004), 789-796 | MR | Zbl

[6] Lapin S. V., “Piecewise-constant stabilization of systems linear in control”, Autom. Remote Control., 53:6 (1992), 816-822 | MR | Zbl

[7] Bourdin L., Trelat E., “Robustness under control sampling of reachability in fixed time for nonlinear control systems”, Math. Control Signals Syst., 33:3 (2021), 515-551 | DOI | MR | Zbl

[8] Zelenyak T. I., Slin'ko M. G., “The dynamics of catalytic systems I”, KICA, 18:5 (1977), 1235-1248 (in Russian)

[9] Zelenyak T. I., Slin'ko M. G., “The dynamics of catalytic systems II”, KICA, 18:6 (1977), 1548-1560 (in Russian)

[10] Musienko E. I., “The control over the solution of a parabolic problem in a neighbourhood of an unstable stationary solution”, Dinamika Sploshn. Sredy, 1981, no. 51, 68-83 (in Russian)

[11] Musienko E. I., “Control of solutions of some parabolic problems in the neighborhood of unstable stationary solutions”, DIEQ, 20:12 (1984), 2120-2130 (in Russian) | Zbl

[12] Ivirsin M. B., “Parametric control of solutions to an evolution problem in a neighborhood of an unstable stationary regime”, SIMJ, 48:4 (2007), 606-615 | MR | Zbl

[13] Ivirsin M. B., “Relay control of an evolution process in a Banach space in a neighborhood of an unstable stationary regime”, SIMJ, 51:1 (2010), 25-37 | MR | Zbl

[14] Kvitko A. N., “A method for solving boundary value problems for nonlinear control systems in the class of discrete controls”, DIEQ, 44:11 (2008), 1559-1570 | MR | Zbl

[15] Kvitko A. N., Yakusheva, D. B., “Solution of the boundary-value problem for nonlinear steady-state controlled system on the infinite time interval considering discrete control function”, Inform. Control Syst., 2011, no. 6, 25-29 (in Russian)

[16] Kvitko A. N., Litvinov, N. N., “Solution of a local boundary problem for a non-linear non-stationary system in the class of discrete controls”, Vestn. St. Petersburg Univ. Prikl. Mat. Inform. Prots. Upr., 18:1 (2022), 18-36 (in Russian)

[17] Sedipkov A. A., “Parametric control of solutions to a linear evolution problem in a neighborhood of an unstable equilibrium”, SIMJ, 60:4 (2019), 685-689 | MR | Zbl

[18] Zorich V. A., Mathematical Analysis, v. II, Springer, Berlin, 2016 | MR | Zbl

[19] Daletskii Yu. L., Krein, M. G., Stability of Solutions of Differential Equations in Banach Space, Amer. Math. Soc., Providence, 1974 | MR | Zbl