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Mathematical Problems in Engineering
Volume 2012, Article ID 581053, 12 pages
http://dx.doi.org/10.1155/2012/581053
Research Article

Exponential Convergence of an Observer Based on Partial Field Measurements for the Wave Equation

MACS Project Team, Inria, France

Received 27 July 2012; Accepted 2 October 2012

Academic Editor: Valery Yakhno

Copyright © 2012 Dominique Chapelle et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [10 citations]

The following is the list of published articles that have cited the current article.

  • C. Bertoglio, D. Chapelle, M.A. Fernández, J.-F. Gerbeau, and P. Moireau, “State observers of a vascular fluid–structure interaction model through measurements in the solid,” Computer Methods in Applied Mechanics and Engineering, vol. 256, pp. 149–168, 2013. View at Publisher · View at Google Scholar
  • Ghislain Haine, “Recovering the observable part of the initial data of an infinite-dimensional linear system with skew-adjoint generator,” Mathematics of Control Signals and Systems, vol. 26, no. 3, pp. 435–462, 2014. View at Publisher · View at Google Scholar
  • Galina C. Garcia, and Takeo Takahashi, “Numerical observers with vanishing viscosity for the 1d wave equation,” Advances in Computational Mathematics, vol. 40, no. 4, pp. 711–745, 2014. View at Publisher · View at Google Scholar
  • Cesare Corrado, Jean-Frédéric Gerbeau, and Philippe Moireau, “Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography,” Journal of Computational Physics, 2014. View at Publisher · View at Google Scholar
  • Nicolae Cîndea, Alexandre Imperiale, and Philippe Moireau, “Data assimilation of time under-sampled measurements using observers, the wave-like equation example,” ESAIM: Control, Optimisation and Calculus of Variations, 2015. View at Publisher · View at Google Scholar
  • Annabelle Collin, Dominique Chapelle, and Philippe Moireau, “A Luenberger observer for reaction–diffusion models with front position data,” Journal of Computational Physics, vol. 300, pp. 288–307, 2015. View at Publisher · View at Google Scholar
  • Sharefa Asiri, Chadia Zayane-Aissa, and Taous-Meriem Laleg-Kirati, “An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation,” Mathematical Problems in Engineering, vol. 2015, pp. 1–8, 2015. View at Publisher · View at Google Scholar
  • Anne-Celine Boulanger, Philippe Moireau, Benoît Perthame, and Jacques Sainte-Marie, “Data assimilation for hyperbolic conservation laws: A Luenberger observer approach based on a kinetic description,” Communications in Mathematical Sciences, vol. 13, no. 3, pp. 587–622, 2015. View at Publisher · View at Google Scholar
  • Atte Aalto, “Output error minimizing back and forth nudging method for initial state recovery,” Systems & Control Letters, vol. 94, pp. 111–117, 2016. View at Publisher · View at Google Scholar
  • Atte Aalto, “Iterative observer-based state and parameter estimation for linear systems,” ESAIM: Control, Optimisation and Calculus of Variations, vol. 24, no. 1, pp. 265–288, 2018. View at Publisher · View at Google Scholar