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Regional gradient observability for semilinear hyperbolic systems: HUM approach

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Abstract

The paper aims to extend the notion of regional observability of the gradient to the semilinear hyperbolic case, in order to reconstruct the gradient of the initial conditions in a subregion ω of the domain evolutionΩ. We start with an asymptotically linear system, the approach is based on an extension of the Hilbert uniqueness method (HUM) and Schauder’s fixed point theorem. The analysis leads to an algorithm which is successfully numerically implemented and illustrated with examples and simulations.

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Author information

Authors and Affiliations

  1. École Nationale de Commerce et de gestion, Sidi Mohamed Ben Abdellah University, Fez, Morocco

    Adil Khazari

  2. TSI Team, MACS Laboratory, Faculty of Sciences, Moulay Ismail University, Meknes, Morocco

    Ali Boutoulout

  3. École nationale supérieure des mines de Rabat, Rabat, Morocco

    Imad El Harraki

Authors
  1. Adil Khazari
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  2. Ali Boutoulout
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  3. Imad El Harraki
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Corresponding author

Correspondence to Ali Boutoulout.

Additional information

This work was supported by Academy Hassan II.

Adil KHAZARI is a professor at the University Sidi Mohamed Ben Abdellah, ´ Ecole Nationale de Commerce et de gestion, Fez -Morocco. He obtained his Ph.D. degree in System Regional Analysis, in 2015 at University Moulay Ismail. E-mail: adil.khazari@usmba.ac.ma.

Ali BOUTOULOUT is a professor at the University Moulay Ismail of Meknes in Morocco. He obtained his Ph.D. degree in System Regional Analysis, in 2000, at University Moulay Ismail. Professor Boutoulout has published many paper in the area of system analysis and control. Currently, he is the head of the research team STI (System Theory and Informatics) and a director of Master System Theory and Informatics, in Department of Mathematics and Informatics of Faculty of Sciences at the University Moulay Ismail, of Meknes in Morocco. E-mail: boutouloutali@yahoo.fr.

Imad EL HARRAKI is a professor at ´ Ecole nationale sup´ erieure des mines, Rabat. He obtained his Ph.D. degree in System Regional Analysis, in 2016, at University Moulay Ismail. E-mail: elharraki@enim.ac.ma.

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Khazari, A., Boutoulout, A. & El Harraki, I. Regional gradient observability for semilinear hyperbolic systems: HUM approach. Control Theory Technol. 16, 72–80 (2018). https://doi.org/10.1007/s11768-018-6122-9

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  • DOI: https://doi.org/10.1007/s11768-018-6122-9

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