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Weak and exact domination in distributed systems

Afifi L., Magri E. M., El Jai A.

International Journal of Applied Mathematics and Computer Science

2010

Vol. 20, no 3

419-426

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.

Enlarged Exact Compensation in Distributed Systems

Afifi L., Chafiai A., Bel Fekih A.

International Journal of Applied Mathematics and Computer Science

2002

Vol. 12, no 4

467-477

In this work, we examine, through the observation of a class of linear distributed systems, the possibility of reducing the effect of disturbances (pollution, etc.), by making observations within a given margin of tolerance using a control term. This problem is called enlarged exact remediability. We show that with a convenient choice of input and output operators (actuators and sensors, respectively), the considered control problem has a unique optimal solution, which will be given. We also study the relationship between the notion of remediability, introduced in previous works, and that of enlarged exact remediability.

Spatial Compensation of Boundary Disturbances by Boundary Actuators

Afifi L., Chafiai A., El Jai A.

International Journal of Applied Mathematics and Computer Science

2001

Vol. 11, no 4

899-920

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.

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

2001

Vol. 11, no 2

319-347

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.