An Asymptotic Analysis of the Gradient Remediability Problem for Disturbed Distributed Linear Systems

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Soraya Rekkab
https://orcid.org/0000-0002-2573-6570
Samir Benhadid
https://orcid.org/0000-0003-4416-4392
Raheam Al-Saphory
https://orcid.org/0000-0003-0253-7058

Abstract

The goal of this work is demonstrating, through the gradient observation of a   of type linear ( -systems), the possibility for reducing the effect of any disturbances (pollution, radiation, infection, etc.) asymptotically, by a suitable choice of related actuators of these systems. Thus, a class of  ( -system) was developed based on finite time  ( -system). Furthermore, definitions and some properties of this concept -system and asymptotically gradient controllable system ( -controllable) were stated and studied. More precisely, asymptotically gradient efficient actuators ensuring the weak asymptotically gradient compensation system ( -system) of known or unknown disturbances are examined. Consequently, under convenient hypothesis, the existence and the uniqueness of the control of type optimal, guaranteeing the asymptotically gradient compensation system ( -system), are shown and proven. Finally, an approach that leads to a Mathematical approximation algorithm is explored.

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1.
Rekkab S, Benhadid S, Al-Saphory R. An Asymptotic Analysis of the Gradient Remediability Problem for Disturbed Distributed Linear Systems. Baghdad Sci.J [Internet]. 2022 Dec. 5 [cited 2023 Jan. 28];19(6(Suppl.):1623. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/6611
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