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

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N.U. Ahmed

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


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