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1
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Weak and exact domination in distributed systems

100%
Afifi L., Magri E. M., El Jai A.
International Journal of Applied Mathematics and Computer Science
|
2010
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tom 20
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nr 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
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Minimization of the total completion time for asynchronous transmission in a packet data-transmission system

100%
Piórkowski A., Werewka J.
International Journal of Applied Mathematics and Computer Science
|
2010
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tom 20
|
nr 2
391-400
EN
The minimization of the total completion time for asynchronous transmission in distributed systems is discussed. Attention is focused on the problem of message scheduling on part of the sender. Messages to be sent form a queue, and the order in which they are to be sent has to be first established. The methods of scheduling messages, which minimize the factor of the total completion time, are presented herein. The message-scheduling problem becomes considerably complicated when the stream of data transmitted between the sender and the receiver is organized into packets. A scheduling rule, according to which the shortest messages (SPT-Shortest Processing Time) are selected as the first to be sent, has been proven to be appropriate for the proposed model. A heuristic algorithm for scheduling messages with real-time constraints is proposed. The performance of the scheduling algorithm is experimentally evaluated. The results of the study show the possibility of improving the total completion time from a few to ten percent, depending on the characteristics of the sender. Thus, the practicability of the method has been proved.
3
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Regional control problem for distributed bilinear systems: Approach and simulations

100%
Ztot K., Zerrik E. H., Bourray H.
International Journal of Applied Mathematics and Computer Science
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2011
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tom 21
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nr 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.
4
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Asynchronous distributed state estimation for continuous-time stochastic processes

100%
Kowalczuk Z., Domżalski M.
International Journal of Applied Mathematics and Computer Science
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2013
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tom 23
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nr 2
327-339
EN
The problem of state estimation of a continuous-time stochastic process using an Asynchronous Distributed multi-sensor Estimation (ADE) system is considered. The state of a process of interest is estimated by a group of local estimators constituting the proposed ADE system. Each estimator is based, e.g., on a Kalman filter and performs single sensor filtration and fusion of its local results with the results from other/remote processors to compute possibly the best state estimates. In performing data fusion, however, two important issues need to be addressed namely, the problem of asynchronism of local processors and the issue of unknown correlation between asynchronous data in local processors. Both the problems, along with their solutions, are investigated in this paper. Possible applications and effectiveness of the proposed ADE approach are illustrated by simulated experiments, including a non-complete connection graph of such a distributed estimation system.
5
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Enlarged exact compensation in distributed systems

88%
Afifi L., Chafiai A., Fekih A. B.
International Journal of Applied Mathematics and Computer Science
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2002
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tom 12
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nr 4
467-477
EN
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.
6
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Sensors and boundary state reconstruction of hyperbolic systems

88%
Zerrik E., Bourray H., Hadid S.
International Journal of Applied Mathematics and Computer Science
|
2010
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tom 20
|
nr 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.
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