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Content available remote Regional control problem for distributed bilinear systems: approach and simulations
Ztot K., Zerrik E. H., Bourray H.
International Journal of Applied Mathematics and Computer Science
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2011
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Vol. 21, no 3
499-508
EN
This paper investigates the regional control problem for infinite dimensional bilinear systems. We develop an approach that characterizes the optimal control and leads to a numerical algorithm. The obtained results are successfully illustrated by simulations.
2
Content available remote Sensors and boundary state reconstruction of hyperbolic systems
Zerrik E. H., Bourray H., Ben Hadid S.
International Journal of Applied Mathematics and Computer Science
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2010
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Vol. 20, no 2
227-238
EN
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.
3
Content available remote An output controllability problem for semilinear distributed hyperbolic systems
Zerrik E., Larhrissi R., Bourray H.
International Journal of Applied Mathematics and Computer Science
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2007
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Vol. 17, no 4
437-446
EN
The paper aims at extending the notion of regional controllability developed for linear systems to the semilinear hyperbolic case. We begin with an asymptotically linear system and the approach is based on an extension of the Hilbert uniqueness method and Schauder’s fixed point theorem. The analytical case is then tackled using generalized inverse techniques and converted to a fixed point problem leading to an algorithm which is successfully implemented numerically and illustrated with examples.
4
Content available remote Gradient Observability for Diffusion Systems
Zerrik E. H., Bourray H.
International Journal of Applied Mathematics and Computer Science
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2003
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Vol. 13, no 2
139-150
EN
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.
5
Content available remote Regional boundary obsevability: A numerical approach
Zerrik E. H., Bourray H., Boutoulout A.
International Journal of Applied Mathematics and Computer Science
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2002
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Vol. 12, no 2
143-151
EN
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.
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