REGIONAL BOUNDARY ASYMPTOTIC GRADIENT FULL ORDER OBSERVER VIA INTERNAL REGION
Keywords:
Γ^* G-strategic sensors, Γ^* AGFO-detectability, Γ^* AGFO-observers, diffusion system.
Abstract
The purpose of this paper is to deals with the problem of regional boundary asymptotic gradient full order observer (-observer) concept by using internal regional case. Thus, we study the relation between this notion and the corresponding asymptotic detectability and sensors. More precisely, various important results have been examined and explored concern an extension of an approach which enables to reconstruct the gradient of current state from internal region. In addition, it has been shown that the characterization of -observability under which conditions to be achieved. Finally, we have illustrate that there is a dynamical system which does not represent the observer in the usual sense, but it could be interpreted as a -observer.
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References
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[25] Burns, J., “Observers and optimal estimation for PDE systems: sensor location problems”, IMA Workshop on Sensor Location in Distributed Parameter Systems, September 6-8, 2017 Minneapolis, MN, USA. 2017.
[26] Zerrik, E. and Ouzahra M., “Output stabilization for infinite-dimensional bilinear systems”, International Journal of Applied Mathematics and computer Science, Vol. 15, No. 2, 187–195, 2005.
[27] Brezis H., "Analyse Fonctionnalle". Theorie et applications. 2em tirage. Masson, Paris, France,1987.
[28] Dautray R.; Lions, J.L. Analyse mathématique et calcul numérique pour les sciences et lestechniques; série scientifique 8, Masson : Paris, 1984.
[29] Curtain, R. F. and Pritchard, A. J., "Infinite dimensional linear systems theory". Lecture Note in Control and Information Sciences, Springer- Verlag, New York, 1978.
[30] Al-Saphory, R. Al-Jawari, N. and Al-Qaisi, A. “Regional gradient detectability for infinite dimensional systems”. Tikrit Journal of Pure Science. Vol. 15, No. 2, 1-6, 2010.
[31] Al-Saphory, R. and Al-Bayati, M., Regional boundary gradient detectability in distributed parameter systems, Journal of Advances in Mathematics, 14 (2), pp. 7817-7833, 2018.
[2] Gressang, R.V., Lamont, G.B., Observers For Characterized by semi-groups, IEEE Trans. Automat. Contr., 1975, 523-528.
[3] El Jai, A., Pritchard, A. j., Sensors and Actuators in Distributed System, International Journal of Control, 1987, Vol. 46, 1139-1153.
[4] El Jai, A., Pritchard A, Sensors and Controls in The Analysis of Distributed Parameter Systems, Ellis Hardwood Series in Mathematics and Applications , Wiley, New York, 1988.
[5] El Jai, A., Amouroux, M., Sensors and Observers in Distributed Parameter Systems, International Journal of Control. Vol. 47, No. 1, 1988, pp.333-347.
[6] El Jai, A.; Simon, M. C.; Zerrik, E. Regional observability and sensor structures. Sensors and Actuators 1993, 39, 95-102.
[7] El Jai, A., Zerrik, E., Simon, M.C, Amouroux, M., Regional Observability of a Thermal Process., IEEE Transactions on Automatic Control 1995, 40, 518-521.
[8] El Jai A., Hamzaoui H., On actuators number in distributed systems, Sensors and Actuators A, 2008, Vol. 147, 273-278.
[9] El Jai A., Hamzaoui H., Regional observation and sensors, International Journal of Applied Mathematics and Computer Sciences, 2009, Vol. 19, 5-14.
[10] Al-Saphory, R., El Jai, A., Sensors Structures and Regional Detectability of Parabolic Distributed System, Sensors and Actuators, 2001, Vol. 29, 163-171.
[11] Al-Saphory, R., El Jai, A, Sensors and Regional Asymptotic ω- observer for Distributed Diffusion Systems, Sensors, 2001, Vol. 1, 161-182.
[12] Al-Saphory, R., El Jai, A., Sensors Characterizations for Regional Boundary Detectability in Distributed Parameter Systems, Sensors and Actuators , 2001, 94 (1-2), 1–10.
[13] Al-Saphory, R., El Jai, A., Regional Asymptotic State Reconstruction, International Journal of System Science, 2002, Vol. 33, 1025-1037.
[14] Al-Saphory, R., Asymptotic Regional Boundary Observer in Distributed Parameter Systems via Sensors Structure, Sensors, 2002 2, 137-152.
[15] Al-Saphory, R., “Strategic sensors and regional exponential observability”. ISRN Applied Mathematics. Vol. 2011. Article ID 673052, 1-13, 2011.
[16] Al-Saphory, R., Analyse régionale asymptotique d'une classe de systèmes distribués, Ph.D. thesis, University of Perpignan, France, 2001, https://books.google.iq/books/about/Analyse_r%C3%A9gionale_asymptotique_d_une_cl.html?id=TrwjOgAACAAJ&redir_esc=y, Books Google, Amazon, 2011.
[17] Zerrik, E. and Bourray H., "Gradient Observability for diffusion Systems". International Journal of Applied Mathematics and Computer Science. Vol. 13, pp. 139-150, 2003.
[18] Boutoulout, A., Bourray, H., and Khazari, A., "Flux observability for hyperbolic systems". Applied Mathematics and Information Sciences Letters”. Vol. 2 , No. 1, 13-24, 2014.
[19] Ben Hadid, S., Rekkab, S., and Zerrik, E., "Sensors and regional gradient observability of hyperbolic systems". Intelligent Control and Automation 3, 78-89, 2012.
[20] Al-Saphory R., Al-Jawari N., Al-Janabi A., Regional boundary gradient strategic sensors characterizations, Mathematical Theory and Modeling, 2016, Vol. 5, No.14, 10-26.
[21] Al-Saphory R., Al-Jawari, N., Al-Janabi, A., Asymptotic regional gradient full-order observer in distributed parabolic systems, International Journal of Contemporary Mathematical Sciences, 2016, Vol. 11, No. 7, 343 – 358.
[22] Al-Saphory R., Al-Jawari N., Al-Janabi A., General asymptotic regional gradient observer, Aust. J. Basic & Appl. Sci., 2016, Vol. 10, No. 9, 8-18.
[23] Borggaard, J. Burns, J. Surana, A. and Zietsman, L. “Control, estimation and optimization of energy efficient buildings”. 2009 American Control Conference. Hyatt regency riverfront, St. Louis, MO, USA, MD, USA. June 10-12, 2009.
[24] Burns, J., Jorggaard, J., Cliff, M. and Zietsman, L, “Optimal sensor design for estimation and optimization of PDE Systems”. 2010 American Control Conference. Marriott Waterfront, Baltimore, MD, USA. June 30-July 02, 2010.
[25] Burns, J., “Observers and optimal estimation for PDE systems: sensor location problems”, IMA Workshop on Sensor Location in Distributed Parameter Systems, September 6-8, 2017 Minneapolis, MN, USA. 2017.
[26] Zerrik, E. and Ouzahra M., “Output stabilization for infinite-dimensional bilinear systems”, International Journal of Applied Mathematics and computer Science, Vol. 15, No. 2, 187–195, 2005.
[27] Brezis H., "Analyse Fonctionnalle". Theorie et applications. 2em tirage. Masson, Paris, France,1987.
[28] Dautray R.; Lions, J.L. Analyse mathématique et calcul numérique pour les sciences et lestechniques; série scientifique 8, Masson : Paris, 1984.
[29] Curtain, R. F. and Pritchard, A. J., "Infinite dimensional linear systems theory". Lecture Note in Control and Information Sciences, Springer- Verlag, New York, 1978.
[30] Al-Saphory, R. Al-Jawari, N. and Al-Qaisi, A. “Regional gradient detectability for infinite dimensional systems”. Tikrit Journal of Pure Science. Vol. 15, No. 2, 1-6, 2010.
[31] Al-Saphory, R. and Al-Bayati, M., Regional boundary gradient detectability in distributed parameter systems, Journal of Advances in Mathematics, 14 (2), pp. 7817-7833, 2018.
Published
2020-03-03
How to Cite
Reaheam, A.-S. (2020). REGIONAL BOUNDARY ASYMPTOTIC GRADIENT FULL ORDER OBSERVER VIA INTERNAL REGION. Al-Qadisiyah Journal of Pure Science, 25(1), math 40- 45. https://doi.org/10.29350/qjps.2020.25.1.1061
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Mathematics
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