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ArticleOriginal scientific text

Title

Controllability of evolution equations and inclusions driven by vector measures

Authors 1

Affiliations

  1. School of Information Technology and Engineering and Department of Mathematics, University of Ottawa, Ottawa, Ontario K1N6N5

Abstract

In this paper, we consider the question of controllability of a class of linear and semilinear evolution equations on Hilbert space with measures as controls. We present necessary and sufficient conditions for weak and exact (strong) controllability of a linear system. Using this result we prove that exact controllability of the linear system implies exact controllability of a perturbed semilinear system. Controllability problem for the semilinear system is formulated as a fixed point problem on the space of vector measures and is concluded controllability from the existence of a fixed point. Our results cover impulsive controls as well as regular controls.

Keywords

ENG
controlability, impulsive systems, differential inclusions, Hilbert spaces, vector valued measures, C₀ semigroups

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Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2004/24/1
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Pages:
49-72
Main language of publication
English
Received
2004-06-01
Published
2004

DOI: 10.7151/dmgt.1052

Exact and natural sciences