Free Access
Issue |
ESAIM: COCV
Volume 21, Number 3, July-September 2015
|
|
---|---|---|
Page(s) | 635 - 669 | |
DOI | https://doi.org/10.1051/cocv/2014042 | |
Published online | 20 May 2015 |
- R.A. Anthes, Data assimilation and initialization of hurricane prediction model. J. Atmospheric Sci. 31 (1974) 702–719. [CrossRef] [Google Scholar]
- H T Banks, K. Ito and C. Wang, Exponentially stable approximations of weakly damped wave equations, in Estimation and control of distributed parameter systems (Vorau, 1990). Birkhäuser, Basel (1991) 1–33. [Google Scholar]
- C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary. SIAM J. Control Optim. 30 (1992) 1024–1065. [Google Scholar]
- A. Bensoussan, Filtrage optimal des systèmes linéaires. Dunod (1971). [Google Scholar]
- J. Blum, F.X. LeDimet and I.N. Navon, Data assimilation for geophysical fluids. In vol. 14 of Handbook of Numerical Analysis: Computational Methods for the Atmosphere and the Oceans. Elsevier, Amsterdam (2008) 377–434. [Google Scholar]
- R. Chabiniok, P. Moireau, P.-F. Lesault, A. Rahmouni, J.-F. Deux and D. Chapelle, Trials on tissue contractility estimation from cardiac cine-MRI using a biomechanical heart model. In vol. 6666, Proc. of FIMH’11. Lect. Notes Compt. Sci. (2011) 304–313. [Google Scholar]
- D. Chapelle, N. Cîndea, M. De Buhan and P. Moireau, Exponential convergence of an observer based on partial field measurements for the wave equation. Math. Probl. Eng. 2012 (2012) 12. [CrossRef] [Google Scholar]
- D. Chapelle, N. Cîndea and P. Moireau, Improving convergence in numerical analysis using observers. The wave-like equation case. Math. Models Methods Appl. Sci. (2012). [Google Scholar]
- D. Chapelle, M. Fragu, V. Mallet and P. Moireau, Fundamental principles of data assimilation underlying the Verdandi library: applications to biophysical model personalization within euHeart. Med. Biol. Eng. Comput. 5 (2013) 1221–1233. [Google Scholar]
- S. Cox and E. Zuazua, The rate at which energy decays in a damped string. Commun. Part. Differ. Eqs. 19 (1994) 213–243. [Google Scholar]
- M. Daoulatli, B. Dehman and M. Khenissi, Local energy decay for the elastic system with nonlinear damping in an exterior domain. SIAM J. Control Optim. 48 (2010) 5254–5275 [CrossRef] [MathSciNet] [Google Scholar]
- G. Evensen, Data Assimilation – The Ensemble Kalman Filter. Springer Verlag (2007). [Google Scholar]
- S. Ervedoza, Spectral conditions for admissibility and observability of wave systems: applications to finite element schemes. Numer. Math. 113 (2009) 377–415. [CrossRef] [MathSciNet] [Google Scholar]
- S. Ervedoza and E. Zuazua, Uniformly exponentially stable approximations for a class of damped systems. J. Math. Pures Appl. 91 (2009) 20–48. [CrossRef] [MathSciNet] [Google Scholar]
- S. Ervedoza, C. Zheng and E. Zuazua, On the observability of time-discrete conservative linear systems. J. functional Anal. 254 (2008) 3037–3078. [CrossRef] [MathSciNet] [Google Scholar]
- G. Haine and K. Ramdani, Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations. Numer. Math. 120 (2012) 307–343. [CrossRef] [MathSciNet] [Google Scholar]
- F.M. Hante, M. Sigalotti and M. Tucsnak, On conditions for asymptotic stability of dissipative infinite-dimensional systems with intermittent damping. J. Differ. Eqs. 252 (2012) 5569–5593. [CrossRef] [Google Scholar]
- A. Haraux and E. Zuazua, Decay estimates for some semilinear damped hyperbolic problems. Arch. Rational Mech. Anal. 100 (1988) 191–206. [CrossRef] [MathSciNet] [Google Scholar]
- J.E. Hoke and R.A. Anthes, The initialization of numerical models by a dynamic-initialization technique (fluid flow models for wind forecasting). Monthly Weather Rev. 104 (1976) 1551–1556. [CrossRef] [Google Scholar]
- R.E. Kalman and R.S. Bucy, New results in linear filtering and prediction theory. J. Basic Eng. 83 (1961) 95–108. [Google Scholar]
- S. Lakshmivarahan and J.M. Lewis, Nudging methods: A critical overview. In vol. XVIII of Data Assimilation for Atmospheric, Oceanic, and Hydrologic Applications. Edited by S.K. Park and L. Xu. Springer (2008). [Google Scholar]
- F.-X. Le Dimet and O. Talagrand, Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus A 38 (2010) 97–110. [Google Scholar]
- X.-D. Li and C.-Z. Xu, Infinite-dimensional Luenberger-like observers for a rotating body-beam system. Systems Control Lett. 60 (2011) 138–145. [CrossRef] [MathSciNet] [Google Scholar]
- K. Liu, Locally distributed control and damping for the conservative systems. SIAM J. Control Optim. 35 (1997) 1574–1590. [Google Scholar]
- D.G. Luenberger, An introduction to observers. IEEE T. Automat. Contr. 16 (1971) 596–602. [CrossRef] [Google Scholar]
- P. Moireau, D. Chapelle and P. Le Tallec. Joint state and parameter estimation for distributed mechanical systems. Comput. Methods Appl. Mech. Engrg. 197 (2007) 659–677. [Google Scholar]
- P. Moireau, D. Chapelle and P. Le Tallec, Filtering for distributed mechanical systems using position measurements: Perspectives in medical imaging. Inverse Probl. 25 (2009) 035010. [CrossRef] [Google Scholar]
- I.M. Navon, Data assimilation for numerical weather prediction: a review. In vol. XVIII of Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications. Edited by S.K. Park and L. Xu. Springer (2009). [Google Scholar]
- N.K. Nichols, Mathematical concepts of data assimilation, in Data Assimilation. Edited by W. Lahoz, B. Khattatov and R. Menard. Springer Berlin Heidelberg (2010) 13–39. [Google Scholar]
- K. Ramdani, T. Takahashi and M. Tucsnak, Uniformly exponentially stable approximations for a class of second order evolution equations-application to LQR problems. ESAIM: COCV 13 (2007) 503–527. [CrossRef] [EDP Sciences] [Google Scholar]
- K. Ramdani, M. Tucsnak and G. Weiss, Recovering the initial state of an infinite-dimensional system using observers. Automatica (2012) 1616–1625. [Google Scholar]
- D. Simon, Optimal state estimation: Kalman, H∞ and nonlinear approaches. Wiley-Interscience (2006). [Google Scholar]
- L.T. Tebou and E. Zuazua, Uniform boundary stabilization of the finite difference space discretization of the 1-d wave equation. Adv. Comput. Math. 26 (2007) 337–365. [Google Scholar]
- D.T. Pham, J. Verron and L. Gourdeau, Singular evolutive kalman filters for data assimilation in oceanography. C. R. Acad. Sci. Paris (1997) 255–260. [Google Scholar]
- M. Tucsnak and G. Weiss, Observation and control for operator semigroups. Birkhäuser Basel (2009). [Google Scholar]
- X. Zhang, C. Zheng and E. Zuazua, Exact controllability of the time discrete wave equation: a multiplier approach. Discret. Contin. Dyn. Syst. (2007) 229–245. [Google Scholar]
- E. Zuazua, Propagation, observation, and control of waves approximated by finite difference methods. SIAM Rev. 47 (2005) 197–243. [CrossRef] [MathSciNet] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.