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1
Content available remote Weak and exact domination in distributed systems
Afifi L., Magri E. M., El Jai A.
International Journal of Applied Mathematics and Computer Science
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2010
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Vol. 20, no 3
419-426
EN
In this work, we introduce and examine the notion of domination for a class of linear distributed systems. This consists in studying the possibility to make a comparison between input or output operators. We give the main algebraic properties of such relations, as well as characterizations of exact and weak domination. We also study the case of actuators, and various situations are examined. Applications and illustrative examples are also given. By duality, we extend this study to observed systems. We obtain similar results and properties, and the case of sensors is equally examined.
2
Content available remote Regional observation and sensors
El Jai A., Hamzaoui H.
International Journal of Applied Mathematics and Computer Science
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2009
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Vol. 19, no 1
5-14
EN
The purpose of this short paper is to provide original results related to the choice of the number of sensors and their supports for general distributed parameter systems. We introduce the notion of extended sensors and we show that the observation error decreases when the support of a sensor is widened. We also show that the observation error decreases when the number of sensors increases.
3
Content available remote How to compensate a spreading disturbance for a class of nonlinear systems
Quaraai Y., Bernoussi A. S., El Jai A.
International Journal of Applied Mathematics and Computer Science
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2008
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Vol. 18, no 2
171-187
EN
We consider a system which is assumed to be affected by an expanding disturbance which occurs at the initial time. The compensation of the disturbance is accomplished by extending the concept of remediability to a class of nonlinear systems. The results are implemented and illustrated with a nonlinear distributed model.
4
Content available remote Spatial Compensation of Boundary Disturbances by Boundary Actuators
Afifi L., Chafiai A., El Jai A.
International Journal of Applied Mathematics and Computer Science
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2001
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Vol. 11, no 4
899-920
EN
In this paper we show how to find convenient boundary actuators, termed boundary efficient actuators, ensuring finite-time space compensation of any boundary disturbance. This is the so-called remediability problem. Then we study the relationship between this remediability notion and controllability by boundary actuators, and hence the relationship between boundary strategic and boundary efficient actuators. We also determine the set of boundary remediable disturbances, and for a boundary disturbance, we give the optimal control ensuring its compensation.
5
Content available remote Regional Detection and Reconstruction of Unknown Internal or Boundary Sources
Afifi L., El Jai A., Merry M.
International Journal of Applied Mathematics and Computer Science
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2001
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Vol. 11, no 2
319-347
EN
The purpose of this paper is to study the problem of regional detection, to characterize internal or boundary regionally detectable sources and regionally spy sensors, and to establish a relationship between these sensors and regionally strategic sensors. It is shown how to reconstruct a regionally detectable internal or a boundary source from a given output, with an extension to the case when the output is affected by an observation error. Numerical results are given in the case of a diffusion system.
6
Content available remote Admissible Disturbance Sets for Discrete Perturbed Systems
Bouyaghroumni J., El Jai A., Rachik M.
International Journal of Applied Mathematics and Computer Science
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2001
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Vol. 11, no 2
349-367
EN
We consider a discrete disturbed system given by the difference bilinear equation x^{w}_{i+1} =Ax^{w}_{i} + De_{i} + sum_{j=1}^{q}f^{j}_{i}B_{j}x^{w}_{i}, i geq 0, where w=((e_{i})_{i geq 0}, (f_{i})_{i geq 0}) are disturbances which excite the system in a linear and a bilinear form. We assume that the system is augmented with the output function y^{w}_{i}=Cx^{w}_{i}, i geq 0. Let varepsilon be a tolerance index on the output. The disturbance w is said to be varepsilon-admissible if ||y^{w}_{i}-y_{i}|| leq varepsilon, forall i geq 0, where (y_{i})_{i geq 0} is the output signal associated with the case of an uninfected system. The set of all varepsilon-admissible disturbances is the admissible set {cal W}(varepsilon). The characterization of {cal W}(varepsilon) is investigated and numerical simulations are given.
7
Content available remote Spreadability and spray actuators
El Yacoubi S., El Jai A., Karrakchou J.
Applied Mathematics and Computer Science
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1998
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Vol. 8, no 2
367-379
EN
Spreadability of distributed systems has been recently introduced (El Jai and Kassara, 1994; El Jai et al., 1995). The aim of this paper is to propose a new approach to spreadability based on considering actuators as generators of spreadability. This approach is related to ecological and environmental problems, like vegetation dynamics, where the actuators are assumed to be governed by a transport equation while the system is described by a diffusion model.
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