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2 International Journal of Applied Mathematics and Computer Science

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Sensors and boundary state reconstruction of hyperbolic systems

Zerrik E. H., Bourray H., Ben Hadid S.

International Journal of Applied Mathematics and Computer Science

2010

Vol. 20, no 2

227-238

This paper deals with the problem of regional observability of hyperbolic systems in the case where the subregion of interest is a boundary part of the system evolution domain. We give a definition and establish characterizations in connection with the sensor structure. Then we show that it is possible to reconstruct the system state on a subregion of the boundary. The developed approach, based on the Hilbert uniqueness method (Lions, 1988), leads to a reconstruction algorithm. The obtained results are illustrated with numerical examples and simulations.

Regional boundary obsevability: A numerical approach

Zerrik E. H., Bourray H., Boutoulout A.

International Journal of Applied Mathematics and Computer Science

2002

Vol. 12, no 2

143-151

In this paper we review the concept of regional boundary observability, developed in (Michelitti, 1976), by means of sensor structures. This leads to the so-called boundary strategic sensors. A characterization of such sensors which guarantees regional boundary observability is given. The results obtained are applied to a two-dimensional system, and various cases of sensors are considered. We also describe an approach which leads to the estimation of the initial boundary state, which is illustrated by simulations.