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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.

Gradient Observability for Diffusion Systems

Zerrik E. H., Bourray H.

International Journal of Applied Mathematics and Computer Science

2003

Vol. 13, no 2

139-150

The aim of this paper is to study regional gradient observability for a diffusion system and the reconstruction of the state gradient without the knowledge of the state. First, we give definitions and characterizations of these new concepts and establish necessary conditions for the sensor structure in order to obtain regional gradient observability. We also explore an approach which allows for a regional gradient reconstruction. The developed method is original and leads to a numerical algorithm illustrated by simulations.