An Asymptotic Analysis of the Gradient Remediability Problem for Disturbed Distributed Linear Systems
Main Article Content
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.
Received 10/10/2021
Accepted 2/10/2022
Published Online First 25/11/2022
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
How to Cite
References
Issa M J, El-Obaidi B S, Muslim R I. Evaluation of Some Trace Elements Pollution in Sediments of the Tigris River in Wasit Governorate, Iraq. Baghdad Sci J. 2020Mar.1; 17(1): 9-22.
https://doi.org/10.21123/bsj.2020.17.1.0009 Salih N, AL-Bakhat Y, Al-Rahmani A, Murbat O, Ameen N, Majed N. Assessment of Radiological Air Contamination for Selected Places at Al-Tuwaitha Nuclear Site during Winter and Spring. Baghdad Sci.J [Internet]. 2018Sep.13; 15(3): 278-286. http://dx.doi.org/10.21123/bsj.2018.15.3.0278.
Talib AH, Abdulateef ZN, Ali ZA Measurement of some Air Pollutantsin Printing Units and Copy Centers Within Baghdad City. Baghdad Sci J. 2021Mar.30; 18(1(Suppl.): 687-694. https://dx.doi.org/10.21123/bsj.2021.18.1(Suppl.).0000
Afifi L, Lasri K, Joundi M, Amimi N. Feedback Controls for Finite Time or Asymptotic Compensation in Lumped Disturbed Systems. J adv Math Comput Sci. 2015;7(3):168-180.
Qaraai Y, Bernoussi A, El Jai A. How to compensate a spreading disturbance for a class of nonlinear systems. Int. J. Appl. Math. Comput Sci. 2008, 18(2):171–187.
Souhaile S, Afifi L. Cheap compensation in distributed linear dynamical systems with multi-input delays. Int. J. Dyn. Control. 2020, (8):243–253. https://doi.org/10.1007/s40435-018-00505-6.
Souhaile S, Afifi L. Minimum energy compensation for discrete delayed systems with disturbances. Discrete Contin Dyn Syst. 2020; 13(9): 2489-2508. https://www.aimsciences.org/article/doi/10.3934/dcdss.2020119.
Afifi L, Bahadi M, El Jai A, El Mizane A. Asymptotic Analysis Approximations and Simulations of the Compensation Problem in Hyperbolic Systems. Applied. Math. Sci. 2009; 3(15): 737-765.
Afifi L, Hakam M, Bahadi M, El Jai A. An enlarged analysis of the asymptotic compensation problem for a class of distributed systems. Int J Appl Math Sci. 2009; 3(31): 1525 - 1555.
Rekkab S, Regional observability of the gradient of hyperbolic systems. PhD [dissertation], Mentouri University Constantine: Algeria; 2014. http://archives.umc.edu.dz/bitstream/handle/123456789/8821/REK6473.pdf?sequence=1
Benhadid S, Rekkab S, Zerrik E. Sensors and boundary gradient observability of hyperbolic systems. Int J Manag Inform Tech. 2013; 4 (3): 295-316.
Rekkab S, Aichaoui H, Benhadid S. Regional Gradient Compensation with Minimum Energy. J Math Mech. 2019; 61:19-31. https://dx.doi.org/10.17223/19988621/61/3
Al-Saphory R, Khalid Z, El-Jai A. Regional Boundary Gradient Closed Loop Control System and Γ*AGFO-Observer. J Phys: Conf Ser. 2020; 1664 (012061): 1-19.
Al-Saphory R, El Jai A. Asymptotic Regional State Reconstruction, Int J Syst Sci. 2002; 33(13): 1025-1037.
Al-Saphory R, Al-Shaya A, Rekkab S. Regional Boundary Asymptotic Gradient Reduced Order Observer. J Phys : Conf Ser. 2020; 1664 (012101): 1-18.