IJPAM: Volume 73, No. 2 (2011)

REGIONAL OBSERVABILITY WITH
CONSTRAINTS OF THE GRADIENT

A. Boutoulout$^1$, H. Bourray$^2$, M. Baddi$^3$
$^{1,2,3}$TSI Team, MACS Laboratory
Faculty of Sciences
Moulay Ismaïl University
Meknes, MOROCCO


Abstract. The aim of this paper is to explore the concept of observability with constraints of the gradient for distributed parabolic system evolving in spatial domain $\Omega$. It consists in the reconstruction of the initial state gradient and must be between two prescribed functions in a subregion $\omega$ of $\Omega$. We give definitions and some properties of this kind of regional observability and we describe two approaches to solve this problem where the first is based on subdifferential techniques and the second uses the lagrangian multiplier method. This last approach leads to an algorithm which is performed by example and simulation.

Received: October 26, 2011

AMS Subject Classification: 93B07, 93C20

Key Words and Phrases: distributed systems, parabolic systems, regional observability, gradient reconstruction

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 73
Issue: 2