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The method of controlled models in the problem of reconstruction of a nonlinear delay system

The method of controlled models in the problem of reconstruction of a nonlinear delay system ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 1, pp. 37–42.  c Pleiades Publishing, Ltd., 2007. Original Russian Text  c V.I. Maksimov, N.A. Fedina, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 1, pp. 36–40. ORDINARY DIFFERENTIAL EQUATIONS TheMethodofControlled Modelsinthe Problem of Reconstruction of a Nonlinear Delay System V. I. Maksimov and N. A. Fedina Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia Received May 31, 2006 DOI: 10.1134/S0012266107010065 We consider the system described by the nonlinear delay differential equation x ˙ (t)= f (x(t),x(t − ν)) + Bu(t),t ∈ [0,T ],x(s)= x (s),s ∈ [−ν, 0], N n where x ∈ R , u ∈ R , ν =const > 0 is the delay, T< +∞, B is an N × n matrix, f is an N × N matrix function satisfying the Lipschitz condition, and the initial state x (s), s ∈ [−τ, 0], is a continuous function. The trajectory x(·) of the system depends on the nonstationary input u(·). Neither the input nor the trajectory is given in advance. It is only known that u(·) is a function whose norm is square integrable; i.e., u(·) ∈ L ([0,T http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

The method of controlled models in the problem of reconstruction of a nonlinear delay system

Maksimov, V.; Fedina, N.
Differential Equations , Volume 43 (1) – Feb 24, 2007
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References (5)

Publisher
Springer Journals
Copyright
Copyright © 2007 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266107010065
Publisher site
See Article on Publisher Site

Abstract

ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 1, pp. 37–42.  c Pleiades Publishing, Ltd., 2007. Original Russian Text  c V.I. Maksimov, N.A. Fedina, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 1, pp. 36–40. ORDINARY DIFFERENTIAL EQUATIONS TheMethodofControlled Modelsinthe Problem of Reconstruction of a Nonlinear Delay System V. I. Maksimov and N. A. Fedina Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia Received May 31, 2006 DOI: 10.1134/S0012266107010065 We consider the system described by the nonlinear delay differential equation x ˙ (t)= f (x(t),x(t − ν)) + Bu(t),t ∈ [0,T ],x(s)= x (s),s ∈ [−ν, 0], N n where x ∈ R , u ∈ R , ν =const > 0 is the delay, T< +∞, B is an N × n matrix, f is an N × N matrix function satisfying the Lipschitz condition, and the initial state x (s), s ∈ [−τ, 0], is a continuous function. The trajectory x(·) of the system depends on the nonstationary input u(·). Neither the input nor the trajectory is given in advance. It is only known that u(·) is a function whose norm is square integrable; i.e., u(·) ∈ L ([0,T

Journal

Differential Equations – Springer Journals

Published: Feb 24, 2007

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