Differential Inclusions, Control and Optimization 24 (2004) 49-72
doi: 10.7151/dmdico.1052

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CONTROLLABILITY OF EVOLUTION EQUATIONS AND INCLUSIONS DRIVEN BY VECTOR MEASURES

N.U. Ahmed

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

2000 Mathematics Subject Classification: 34G20, 34K30, 35A05, 35B30, 93C25.

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Received 1 June 2004