Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

On the Existence of an Optimal Control in a Nonlinear Minimum Time Problem

On the Existence of an Optimal Control in a Nonlinear Minimum Time Problem Differential Equations, Vol. 40, No. 2, 2004, pp. 184–189. Translated from Differentsial'nye Uravneniya, Vol. 40, No. 2, 2004, pp. 177–182. Original Russian Text Copyright c 2004 by Topunov. ORDINARY DIFFERENTIAL EQUATIONS On the Existence of an Optimal Control in a Nonlinear Minimum Time Problem M. V. Topunov Moscow Pedagogical State University, Moscow, Russia Received September 5, 2002 1. STATEMENT OF THE PROBLEM Consider a smooth nonlinear control system x _ = f (x;u);x 2 M;u 2 U; (1:1) 1 n m where M is a C manifold regularly embedded in R , U is a convex compact polyhedron in R , n 2 and f : M  U ! R is a C mapping satisfying the following condition: there exist smooth functionals a (x;u): M  U ! R ij such that @ f (x;u) @f (x;u) (w ;w )= a (x;u) w;i;j =1;:::;M; (1:2) i j k ij @u @u k=1 where w ;:::;w are linearly independent vectors tangent to the relative interiors of the respective 1 M edges ;:::; of U and possessing the property 1 M span fw ;:::;w g =span U: (1:3) 1 M R R Note that condition (1.2) is satis http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

On the Existence of an Optimal Control in a Nonlinear Minimum Time Problem

Topunov, M.
Differential Equations , Volume 40 (2) – Oct 18, 2004
Download PDF
6 pages

Loading next page...
 
/lp/springer-journals/on-the-existence-of-an-optimal-control-in-a-nonlinear-minimum-time-bCP009cNPv

References (2)

Publisher
Springer Journals
Copyright
Copyright © 2004 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/B:DIEQ.0000033707.79341.5c
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 40, No. 2, 2004, pp. 184–189. Translated from Differentsial'nye Uravneniya, Vol. 40, No. 2, 2004, pp. 177–182. Original Russian Text Copyright c 2004 by Topunov. ORDINARY DIFFERENTIAL EQUATIONS On the Existence of an Optimal Control in a Nonlinear Minimum Time Problem M. V. Topunov Moscow Pedagogical State University, Moscow, Russia Received September 5, 2002 1. STATEMENT OF THE PROBLEM Consider a smooth nonlinear control system x _ = f (x;u);x 2 M;u 2 U; (1:1) 1 n m where M is a C manifold regularly embedded in R , U is a convex compact polyhedron in R , n 2 and f : M  U ! R is a C mapping satisfying the following condition: there exist smooth functionals a (x;u): M  U ! R ij such that @ f (x;u) @f (x;u) (w ;w )= a (x;u) w;i;j =1;:::;M; (1:2) i j k ij @u @u k=1 where w ;:::;w are linearly independent vectors tangent to the relative interiors of the respective 1 M edges ;:::; of U and possessing the property 1 M span fw ;:::;w g =span U: (1:3) 1 M R R Note that condition (1.2) is satis

Journal

Differential Equations – Springer Journals

Published: Oct 18, 2004

There are no references for this article.