Sensors and boundary state reconstruction of hyperbolic systems

El Zerrik; Hamid Bourray; Samir Ben Hadid

doi:10.2478/v10006-010-0016-4

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Sensors and boundary state reconstruction of hyperbolic systems

International Journal of Applied Mathematics and Computer Science

Volume 20 (2010): Issue 2 (June 2010)

By: El Zerrik, Hamid Bourray and Samir Ben Hadid

Open Access

|Jul 2010

Abstract

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.

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