Regional Boundary Asymptotic Gradient Full-Order Observer in Distributed Parabolic Systems

Authors

  • Raheam Al-Saphory Tikrit University
  • Zinah A. Khalid Tikrit University, Tikrit, Iraq

DOI:

https://doi.org/10.24297/jam.v18i.8543

Keywords:

RBG-Strategic Sensors, RBAG-Detectability, RBAGFO-Observers, Diffusion System

Abstract

The purpose of this paper is to explore the concept of the regional boundary asymptotic gradient full order observer (RBAGFO-observer) in connection with the characterizations of sensors structures. Then, we present various results related to different types of measurements, domains and boundary conditions for distributed parameter systems (DPSS) in parabolic systems problem.  The considered approach of this work is derived from Luenberger observer theory which is enable to estimate asymptotically the state gradient of the original system on a sub-region of the domain boundary  in order that the RBAGFO-observability notion to be achieved. We also show that there exists a dynamical system for the considered system is not BAGFO-observer in the usual sense, but it may be regional RBAGFO-observer.

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Author Biographies

Raheam Al-Saphory, Tikrit University

Department of Mathematics, College of Education for Pure Sciences, Tikrit University, Tikrit, Iraq.

Zinah A. Khalid, Tikrit University, Tikrit, Iraq

Department of Mathematics, College of Education for Pure Sciences

References

B. Friedland, Full-order state observer, Control Systems, Robotic and Automation, 10 (1996). https://www.eolss.net/Sample-Chapters/C18/E6-43-13-08.pdf

R. Al-Saphory, Strategic sensors and regional exponential observability, ISRN Applied Mathematics, (2011), 1-13. https://www.hindawi.com/journals/isrn/2011/673052/

R. Al-Saphory and Sh. Al-Mullah, Regional Exponential Reduced Observability in Distributed Parameter Systems, Journal of Advance in Mathematics, 11 (2015), 5058-5074. https://rajpub.com/index.php/jam/article/view/1256

R. Al-Saphory and Z. Jaafar, Regional exponential general observability in distributed parameter systems, Journal of Advance in Mathematics, 11 (2015), 5166-5182.

https://www.scribd.com/document/283351193/REGIONAL-EXPONENTIAL-GENERAL-OBSERVABILITY-IN-DISTRIBUTED-PARAMETER-SYSTEMS

D. G. Luenberger, Observers For multivariable systems, IEEE Trans. Automat. Contr., 11 (2) (1966), 190-197. https://ieeexplore.ieee.org/document/1098323

R.V. Gressang and G.B. Lamont, Observers for characterized by semi-groups, IEEE Trans. Automat. Contr., 20 (1975), 523-528. https://ieeexplore.ieee.org/document/1101021

A. El Jai and M. Amouroux, Sensors and observers in distributed parameter systems, International Journal of Control., 47 (1988), 333-347.

https://www.tandfonline.com/doi/abs/10.1080/00207178808906013

R. Al-Saphory, M. Al-Joubory and M. Jasim, Regional strategic sensors characterizations, Journal Mathematical and Computational Science, 3 (2013), 401-418.

http://scik.org/index.php/jmcs/article/view/810

A. El Jai and H. Hamzauoi, Regional observation and sensors, International Journal of Applied Mathematics and Computer Sciences, 19 (2009), 5-14.

https://www.sciencedirect.com/science/article/abs/pii/092442479380204T

A. El Jai, M. C. Simon and E. Zerrik, Regional observability and sensor structure, Sensors and Actuators A: Physical, 39 (1993), 95-102.

https://www.sciencedirect.com/science/article/abs/pii/092442479380204T

R. Al-Saphory, N. Al-Jawari and A. Al-Janabi, Regional gradient strategic sensors characterization, Journal of Advanced in Mathematics, 10 (2015), 3605-3618.

https://rajpub.com/index.php/jam/article/view/1735

E. Zerrik and H. Bourray, Gradient observability for diffusion systems, International Journal of Applied Mathematics and Computer Sciences, 2 (2003), 139-150.

http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-amcv13i2p139bwm

R. Al-Saphory, Asymptotic regional analysis for a class of distributed parameter systems, Ph.D. thesis, University of Perpignan, France, 2001, published in French, Amazon Google books, 2011.

https://books.google.iq/books/about/Analyse_r%C3%A9gionale_asymptotique_d_une_cl.html?id=TrwjOgAACAAJ&redir_esc=y

R. Al-Saphory and A. El Jai, Regional Asymptotic State Reconstruction, International Journal of System Science, 33 (2002), 1025-1037.

https://www.tandfonline.com/doi/abs/10.1080/00207720210166998

R. Al-Saphory, N. Al-Jawari and A. Al-Janabi, General asymptotic Regional gradient observer, Aust. J. Basic and Appl. Sci., 10 (2016), 8-18.

http://www.ajbasweb.com/old/ajbas_May_2016.html

R. Al-Saphory and A. El-Jai, Sensors and asymptotic ω-observer for distributed diffusion system, Sensors, 1 (2001), 161-182. https://www.mdpi.com/1424-8220/1/5/161/htm

J. Borggaard, J. Burns, A. Surana and L. Zietsman, Control, estimation and optimization of energy efficient buildings, Proc. of the American Control Conference, Hyatt Regency Riverfront, St. Louis, (2009), 837-841. https://ieeexplore.ieee.org/document/5160552

R Al-Saphory and M Al-Bayati, Regional boundary gradient detectability in distributed parameter systems, Journal of Advances in Mathematics, 14 (2), (2018), 7818-7833.

https://rajpub.com/index.php/jam/article/view/7478

A. El Jai, Distributed systems analysis via sensors and actuators. Sensors and Actuators A, 29,(1), (1991), 1-11.

https://www.sciencedirect.com/science/article/abs/pii/092442479180026L

R. Curtain, and |H. Zwart, An introduction to infinite dimensional linear system theory, Springer-Verlag, New York, 1995. https://www.springer.com/gp/book/9780387944753

R. F. Curtain, and A. J. Pritchard, Infinite dimensional linear systems theory, Lecture Note in Control and Information Sciences, Springer- Verlag, New York, 1978.

https://www.springer.com/gp/book/9783540089612

Burns, J., Observers and ooptimal estimation for PDE ssystems: sensor location problems, IMA Workshop on Sensor Location in Distributed Parameter Systems, September 6-8, 2017 Minneapolis, MN, USA. 2017. https://www.ima.umn.edu/2017-2018/SW9.6-8.17/26444

Brezis H., Analyse Fonctionnalle, Theorie et applications, 2em tirage, Masson, Paris, France,1987. https://www.dunod.com/sciences-techniques/analyse-fonctionnelle-theorie-et-applications

A. El Jai and A.J. Pritchard, Sensors and Controls in the Analysis of Distributed Parameter Systems, Ellis Hardwood Series in Mathematics and Applications, Wiley, New York, 1988.

https://www.ebay.co.uk/itm/Sensors-and-Controls-in-the-Analysis-of-Distributed-Systems-Mathematics-and-its/153079971972?epid=91726288&hash=item23a4470084:i:153079971972

R. Al-Saphory and A. El-Jai, Sensors structures and regional detectability of parabolic distributed system, Sensors and Actuators A: Physical, 90, (2001), 163-171.

https://www.sciencedirect.com/science/article/abs/pii/S0924424701005234

Al-Saphory, R. and El Jai, A., Sensors characterizations for regional boundary detectability in distributed parameter systems, Sensors and Actuators A, 94( 1-2), 2001, 1-10.

https://www.sciencedirect.com/science/article/abs/pii/S0924424701006690

R. Al-Saphory, N. Al-Jawari and A. Al-Janabi, Regional boundary gradient strategic sensors characterizations, Mathematical Theory and Modeling, 6 (2016), 10-26.

https://www.iiste.org/Journals/index.php/MTM/article/view/28228

El Jai, A.; Pritchard, A. J. Sensors and actuators in distributed parameter systems, International Journal of Control., 46, 1987, 1139-1153.

https://www.tandfonline.com/doi/abs/10.1080/00207178708933956?journalCode=tcon20

E. Zerrik, L. Badraoui, A. El Jai, Sensors and regional boundary state reconstruction of parabolic systems. Sensors and Actuators A, 75 (1999), 102-117.

http s://www.sciencedirect.com/science/article/abs/pii/S0924424798002933

R. Al-Saphory, Strategic sensors and regional exponential observability. ISRN Applied Mathematics, 2011. Article ID 673052, 1-13, 2011.

https://www.hindawi.com/journals/isrn/2011/673052/

R. Al-Saphory, Strategic sensors and regional observation in Neumann boundary conditions, Zanco Journal of Pure and Applied Science, Salahaddin University-Hawler/Iraq, 2010.

https://www.academia.edu/35033214/Regional_Asymptotic_Approach_for_Dynamical_Free_Systems

Published

2020-01-14

How to Cite

Al-Saphory, R., & A. Khalid, Z. (2020). Regional Boundary Asymptotic Gradient Full-Order Observer in Distributed Parabolic Systems. JOURNAL OF ADVANCES IN MATHEMATICS, 18, 28-45. https://doi.org/10.24297/jam.v18i.8543

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Articles