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Approximate controllability of infinite dimensional bilinear systems

Approximate controllability of infinite dimensional bilinear systems The aim of this paper is to study approximate controllability for bilinear systems in the general case. The existence and uniqueness of solutions to bilinear evolution equations are obtained. The paper shows that the approximate controllability of the bilinear control problem is equivalent to the approximate controllability of a discrete problem, using the method developed by Loreti and Siconolfi to approximate the bilinear control problem in an infinite-dimensional Banach space by means of a sequence of discrete problems. Finally, the necessary conditions for the bilinear system to be approximately controllable are state and proved. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Approximate controllability of infinite dimensional bilinear systems

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Publisher
Springer Journals
Copyright
Copyright © 1998 by Science Press
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02677349
Publisher site
See Article on Publisher Site

Abstract

The aim of this paper is to study approximate controllability for bilinear systems in the general case. The existence and uniqueness of solutions to bilinear evolution equations are obtained. The paper shows that the approximate controllability of the bilinear control problem is equivalent to the approximate controllability of a discrete problem, using the method developed by Loreti and Siconolfi to approximate the bilinear control problem in an infinite-dimensional Banach space by means of a sequence of discrete problems. Finally, the necessary conditions for the bilinear system to be approximately controllable are state and proved.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 3, 2007

References