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On categories and foundations of the theory of nonlinear control dynamical systems: VI

On categories and foundations of the theory of nonlinear control dynamical systems: VI ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 11, pp. 1490–1494.  c Pleiades Publishing, Ltd., 2007. Original Russian Text  c V.I. Elkin, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 11, pp. 1454–1459. ORDINARY DIFFERENTIAL EQUATIONS On Categories and Foundations of the Theory of Nonlinear Control Dynamical Systems: VI V. I. Elkin Computer Center, Russian Academy of Sciences, Moscow, Russia Received July 4, 2007 DOI: 10.1134/S001226610711002X The present paper is a continuation of [1–5]. In [1], we considered some constructions that can be used when developing the theory of nonlinear dynamical control systems. Such constructions are used (either explicitly or implicitly) in any mathematical theory (group theory, theory of linear spaces, etc.). They are of categorical character. These are morphisms, i.e., mappings relating control systems, and reduced systems (isomorphic systems, subsystems, and quotient systems); in other words, they are, in a sense, simplified models of the original control system. In [1], we also represented a mathematical technique for the analysis of such constructions for nonlinear control systems; this technique is of differential-geometric and group-theoretic character. In [2], we use the notion of a quotient system in a certain category of nonlinear control systems to solve a http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

On categories and foundations of the theory of nonlinear control dynamical systems: VI

Elkin, V.
Differential Equations , Volume 43 (11) – Mar 24, 2007
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References (2)

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/S001226610711002X
Publisher site
See Article on Publisher Site

Abstract

ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 11, pp. 1490–1494.  c Pleiades Publishing, Ltd., 2007. Original Russian Text  c V.I. Elkin, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 11, pp. 1454–1459. ORDINARY DIFFERENTIAL EQUATIONS On Categories and Foundations of the Theory of Nonlinear Control Dynamical Systems: VI V. I. Elkin Computer Center, Russian Academy of Sciences, Moscow, Russia Received July 4, 2007 DOI: 10.1134/S001226610711002X The present paper is a continuation of [1–5]. In [1], we considered some constructions that can be used when developing the theory of nonlinear dynamical control systems. Such constructions are used (either explicitly or implicitly) in any mathematical theory (group theory, theory of linear spaces, etc.). They are of categorical character. These are morphisms, i.e., mappings relating control systems, and reduced systems (isomorphic systems, subsystems, and quotient systems); in other words, they are, in a sense, simplified models of the original control system. In [1], we also represented a mathematical technique for the analysis of such constructions for nonlinear control systems; this technique is of differential-geometric and group-theoretic character. In [2], we use the notion of a quotient system in a certain category of nonlinear control systems to solve a

Journal

Differential Equations – Springer Journals

Published: Mar 24, 2007

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