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

Authors

Soraya Rekkab, Department of Mathematics, Faculty of Exact Science, University of Mentouri, Constantine, Algeria.Follow
Samir Benhadid, Department of Mathematics, Faculty of Exact Science, University of Mentouri, Constantine, Algeria.Follow
Raheam Al-Saphory, Department of Mathematics, College of Education for Pure Sciences, University of Tikrit, Tikrit, Iraq.Follow

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.

Keywords

Asymptotic analysis, Controllability, Disturbance, Optimal control, Remediability

Article Type

Supplemental Issue

How to Cite this Article

Rekkab, Soraya; Benhadid, Samir; and Al-Saphory, Raheam (2022) "An Asymptotic Analysis of the Gradient Remediability Problem for Disturbed Distributed Linear Systems," Baghdad Science Journal: Vol. 19: Iss. 6, Article 25.
DOI: https://doi.org/10.21123/bsj.2022.6611