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Controllability of nonlinear systems with constrained controls

Controllability of nonlinear systems with constrained controls ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 11, pp. 1515–1523.  c Pleiades Publishing, Inc., 2006. Original Russian Text  c A.V. Arutyunov, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 11, pp. 1443–1451. ORDINARY DIFFERENTIAL EQUATIONS Controllability of Nonlinear Systems with Constrained Controls A. V. Arutyunov Russian University of Nations’ Friendship, Moscow, Russia Received May 22, 2006 DOI: 10.1134/S0012266106110012 STATEMENT OF THE PROBLEM Consider the following system of differential equations with a control: x ˙ = f (x, u, t),t ∈ [t ,t ],x (t )= x ,u(t) ∈ U (t) ∀t. (1) 0 1 0 0 Here t ∈ [t ,t ]istime, t <t are given, x is a phase variable ranging in the n-dimensional 0 1 0 1 n m arithmetic space R , u ∈ R is a control parameter, and the symbol ∀ is treated as “almost all.” n m n The initial point x is given. The vector function f : R × R × [t ,t ] → R is twice continuously 0 0 1 differentiable with respect to (x, u) for almost all t, and in addition, this function, together with its partial derivatives of order ≤ 2 with http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Controllability of nonlinear systems with constrained controls

Arutyunov, A.
Differential Equations , Volume 42 (11) – Jan 3, 2006
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References (6)

Publisher
Springer Journals
Copyright
Copyright © 2006 by Pleiades Publishing, Inc.
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266106110012
Publisher site
See Article on Publisher Site

Abstract

ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 11, pp. 1515–1523.  c Pleiades Publishing, Inc., 2006. Original Russian Text  c A.V. Arutyunov, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 11, pp. 1443–1451. ORDINARY DIFFERENTIAL EQUATIONS Controllability of Nonlinear Systems with Constrained Controls A. V. Arutyunov Russian University of Nations’ Friendship, Moscow, Russia Received May 22, 2006 DOI: 10.1134/S0012266106110012 STATEMENT OF THE PROBLEM Consider the following system of differential equations with a control: x ˙ = f (x, u, t),t ∈ [t ,t ],x (t )= x ,u(t) ∈ U (t) ∀t. (1) 0 1 0 0 Here t ∈ [t ,t ]istime, t <t are given, x is a phase variable ranging in the n-dimensional 0 1 0 1 n m arithmetic space R , u ∈ R is a control parameter, and the symbol ∀ is treated as “almost all.” n m n The initial point x is given. The vector function f : R × R × [t ,t ] → R is twice continuously 0 0 1 differentiable with respect to (x, u) for almost all t, and in addition, this function, together with its partial derivatives of order ≤ 2 with

Journal

Differential Equations – Springer Journals

Published: Jan 3, 2006

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