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A Finite-Dimensional Approximation Method in Optimal Control Theory

A Finite-Dimensional Approximation Method in Optimal Control Theory Differential Equations, Vol. 39, No. 11, 2003, pp. 1519–1528. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 11, 2003, pp. 1443–1451. Original Russian Text Copyright c 2003 by Arutyunov, Vinter. ORDINARY DIFFERENTIAL EQUATIONS A Finite-Dimensional Approximation Method in Optimal Control Theory A. V. Arutyunov and R. B. Vinter Friendship of Nations University, Moscow, Russia Imperial College, London, England Received June 10, 2003 1. STATEMENT OF THE PROBLEM Consider the following classical optimal control problem P : minimize the functional J (p;u)= K (p)+ f (t;x(t);u(t))dt; p =(x ;x ) ; 0 S T x = x(S);x = x(T ); S T 1;1 n m over all x 2 W ([S;T ]; R )and u 2 L ([S;T ]; R ) satisfying the constraints x _ (t)= f (t;x(t), u(t)), u(t) 2 U (t) for almost all t 2 [S;T ], K (p)  0, and K (p)=0. Here [S;T]isagiven time 1 2 0 n m n m n 2n 2n k interval, f :[S;T ] R  R ! R, f :[S;T ] R  R ! R , K : R ! R, K : R ! R , 0 1 2n k and K : R ! R http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

A Finite-Dimensional Approximation Method in Optimal Control Theory

Arutyunov, A.; Vinter, R.
Differential Equations , Volume 39 (11) – Oct 5, 2004
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References (3)

Publisher
Springer Journals
Copyright
Copyright © 2003 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.0000019343.83034.9d
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 39, No. 11, 2003, pp. 1519–1528. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 11, 2003, pp. 1443–1451. Original Russian Text Copyright c 2003 by Arutyunov, Vinter. ORDINARY DIFFERENTIAL EQUATIONS A Finite-Dimensional Approximation Method in Optimal Control Theory A. V. Arutyunov and R. B. Vinter Friendship of Nations University, Moscow, Russia Imperial College, London, England Received June 10, 2003 1. STATEMENT OF THE PROBLEM Consider the following classical optimal control problem P : minimize the functional J (p;u)= K (p)+ f (t;x(t);u(t))dt; p =(x ;x ) ; 0 S T x = x(S);x = x(T ); S T 1;1 n m over all x 2 W ([S;T ]; R )and u 2 L ([S;T ]; R ) satisfying the constraints x _ (t)= f (t;x(t), u(t)), u(t) 2 U (t) for almost all t 2 [S;T ], K (p)  0, and K (p)=0. Here [S;T]isagiven time 1 2 0 n m n m n 2n 2n k interval, f :[S;T ] R  R ! R, f :[S;T ] R  R ! R , K : R ! R, K : R ! R , 0 1 2n k and K : R ! R

Journal

Differential Equations – Springer Journals

Published: Oct 5, 2004

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