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Ghislain HAINE > Research

Research

mercredi 25 mai 2016.

Toutes les versions de cet article : [English] [français]

 Brief overview

The main idea of my research is to apply to infinite-dimensional systems (i.e. to Partial Differential Equations) the known results in finite dimension (i.e. in Control) on Luenberger’s observers.

I use GMSH and GetDP for the most of my numerical simulations on observers, and contribute to Wiki OneLAB.

I also use FreeFem++ for my work on fluid dynamics.

You can follow my profile on :

Ghislain Haine   Google Scholar

In my PhD Thesis, I was interested in inverse problems for linear systems by the observers based algorithm introduced by Ramdani, Tucsnak et Weiss (Recovering the initial state of an infinite-dimensional system using observers, Automatica, vol. 46, pp. 1616-1625, 2010). Such problems arise for instance in medical imaging, meteorology, source identification and much more.

 My research interest

 The construction and use of observers in general

In the following example, we reconstruct the observable part of the initial state of a 3D acoustic wave, mesured on a very coarse grid.

The initial data is on the first line. On the second line, you’ll find the reconstruction from the measurement done on the coarse grid (the figure above), with noise.

 The observation and control of fluid flow and fluid-structure interaction

In the following simulation, we control a flow past a rigid beam to stabilize it around a unstable stationary state, by succion and aspiration at the end of the beam (2 active controls).

MPEG4 - 10.2 Mo
Stabilization of a flow past a rigid beam

 Submitted publication(s)

 Published publications

Number of items: 16.

Article

Haine, Ghislain Recovering the observable part of the initial data of an infinite-dimensional linear system with skew-adjoint generator. (2014) Mathematics of Control, Signals, and Systems. ISSN 0932-4194

Haine, Ghislain and Ramdani, Karim Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations. (2012) Numerische Mathematik, vol. 120 (n° 2). pp. 307-343. ISSN 0029-599X

Haine, Ghislain and Ramdani, Karim Observateurs itératifs en horizon fini. Application à la reconstruction de données initiales pour des EDP d'évolution. (2011) Journal Européen des Systèmes Automatisés (JESA), vol. 45 (n°7-10). pp. 715-724. ISSN 1269-6935

Conference or Workshop Item

Haine, Ghislain An observer-based approach for thermoacoustic tomography. (2014) In: The 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), 7 July 2014 - 11 July 2014 (Groningen, Netherlands).

Haine, Ghislain Reconstruction de la partie observable de l'état initial d'un système linéaire conservatif. (2014) In: Workshop Observateurs, 10 April 2014 - 11 April 2014 (Nancy, France). (Unpublished)

Haine, Ghislain Recovering the initial state of a Well-Posed Linear System with skew-adjoint generator. (2014) In: Workshop New trends in modeling, control and inverse problems, 16 June 2014 - 19 June 2014 (Toulouse, France). (Unpublished)

Haine, Ghislain Solving Thermoacoustic Tomography with an observer-based algorithm. (2014) In: Journées Ondes du Sud-Ouest, 5 February 2014 - 7 February 2014 (Toulouse, France). (Unpublished)

Haine, Ghislain Reconstructing initial data using iterative observers for wave type systems. (2013) In: 11th International Conference on Mathematical and Numerical Aspects of Waves (WAVES 2013), 03-07 Jun 2013, Gammarth, Tunisia .

Haine, Ghislain Recovering the initial state of dynamical systems using observers. (2013) In: 8th workshop on Control of Distributed Parameter Systems - CDPS'13, 01-05 Jul 2013 , Craiova, Romania . (Unpublished)

Haine, Ghislain and Phung, Kim Dang and Ramdani, Karim Iterative observers for inverse problems. (2011) In: Conference of the European GDR Control of PDEs, 21-23 Nov 2011, Marseille, France . (Unpublished)

Haine, Ghislain and Ramdani, Karim Reconstructing initial data using iterative observers for wave type systems. A numerical analysis. (2011) In: The 10th International Conference on the Mathematical and Numerical Aspects of Waves (WAVES 2011), 25-29 Jul 2011, Vancouver, Canada .

Invited Conference

Haine, Ghislain and Raymond, Jean-Pierre Simulations of control for Navier-Stokes equations. (2016) In: Congrès CANUM 2016 43e Congrès National d'Analyse Numérique, 9 May 2016 - 13 May 2016 (Obernai, France). (Unpublished)

Haine, Ghislain Recovering the observable part of the initial data of an infinite-dimensional linear system with perturbed skew-adjoint generator using observers. (2015) In: 2015 European Control Conference (ECC), 15 July 2015 (Linz, Austria).

Other Conference

Haine, Ghislain Reconstruction de la partie observable de la donnée initiale d'un système linéaire. (2012) In: Séminaire de mathématiques appliquées, 13 Dec 2012, Clermont-Ferrand, France . (Unpublished)

Haine, Ghislain and Phung, Kim Dang and Ramdani, Karim Observateurs itératifs pour Maxwell. (2011) In: Journée Thématique Problèmes Inverses de la Fédération Charles Hermite, 07 Jun 2011, Nancy, France . (Unpublished)

Thesis

Haine, Ghislain. Observateurs en dimension infinie. Application à l'étude de quelques problèmes inverses. PhD, Applied Mathematics, Université de Lorraine, Nancy, 2012, 192 p.

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