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2 International Journal of Applied Mathematics and Computer Science

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An output controllability problem for semilinear distributed hyperbolic systems

Zerrik E., Larhrissi R., Bourray H.

International Journal of Applied Mathematics and Computer Science

2007

Vol. 17, no 4

437-446

The paper aims at extending the notion of regional controllability developed for linear systems to the semilinear hyperbolic case. We begin with an asymptotically linear system and the approach is based on an extension of the Hilbert uniqueness method and Schauder’s fixed point theorem. The analytical case is then tackled using generalized inverse techniques and converted to a fixed point problem leading to an algorithm which is successfully implemented numerically and illustrated with examples.

Regional Gradient Controllability of Parabolic Systems

Zerrik E., Boutoulout A., Kamal A.

International Journal of Applied Mathematics and Computer Science

1999

Vol. 9, no 4

767-787

The purpose of this paper is to show for parabolic systems how one can achieve a final gradient in a subregion w of the system domain W. First, we give a definition and delineate some properties of this new concept, and then we introduce the concept of regionally gradient strategic actuators. The importance of the spatial structure and location of the actuators in achieving regional gradient controllability is emphasized. Consequently, we concentrate on the determination of a control which would realize a given final gradient on w with minimum energy. The developed approach is original and leads to numerical algorithms for constructing optimal controls. This approach is also illustrated by an example.