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Gradient observability for diffusion systems

100%

Zerrik E. H. , Bourray H.

nr 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.

A new approach to the constrained controllability problem

80%

Boutoulout A. , Ezzahri L. , Bourray H.

nr 2-3

221-228

We consider the problem of internal regional controllability with output constraints. It consists in steering a hyperbolic system to a final state between two prescribed functions only on a subregion of the evolution system domain. This problem is solved by characterizing the optimal control in terms of a subdifferential associated with the minimized functional.

Regional boundary observability: a numerical approach

80%

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

nr 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.