EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 28 (2022) ESAIM: COCV, 28 (2022) 78 References
Open Access
Issue
ESAIM: COCV
Volume 28, 2022
Article Number 78
Number of page(s) 41
DOI https://doi.org/10.1051/cocv/2022071
Published online 22 December 2022
  1. A. Aalto, Convergence of discrete-time Kalman filter estimate to continuous time estimate. Int. J. Control 89 (2016) 668–679. [CrossRef] [Google Scholar]
  2. F. Alouges and M. Aussal, FEM and BEM simulations with the gypsilab framework. SMAI J. Comput. Math. 4 (2018) 297–318. [CrossRef] [MathSciNet] [Google Scholar]
  3. W. Arendt, Heat kernels, Technical report, ISEM course, 2005-2006. [Google Scholar]
  4. J.P. Aubin, Applied Functional Analysis, 2nd ed. Wiley (2000). [Google Scholar]
  5. U. Baur, P. Benner and L. Feng, Model order reduction for linear and nonlinear systems: a system-theoretic perspective. Arch. Comput. Methods Eng. 21 (2014) 331–358. [CrossRef] [MathSciNet] [Google Scholar]
  6. W. Bebendorf and M. Hackbusch, Existence of H-matrix approximants to the inverse FE-matrix of elliptic operators with L1-coefficients. Numer. Math. 95 (2003) 1–28. [CrossRef] [MathSciNet] [Google Scholar]
  7. A. Bensoussan, Filtrage optimal des systèmes linéaires. Dunod (1971). [Google Scholar]
  8. A. Bensoussan, Estimation and Control of Dynamical Systems. Interdisciplinary Applied Mathematics. Springer, Cham (2018). [CrossRef] [Google Scholar]
  9. A. Bensoussan, M.C. Delfour, G. Da Prato and S.K. Mitter, Representation and Control of Infinite Dimensional Systems, second edition. Birkhauser Verlag, Boston (2007). [Google Scholar]
  10. S. Börm, volume 14 Efficient numerical methods for non-local operators: H2-matrix compression, algorithms and analysis. European Mathematical Society (2010). [Google Scholar]
  11. S. Borm, L. Grasedyck and W. Hackbusch, Introduction to hierarchical matrices with applications. Eng. Anal. Boundary Elem. 27 (2003) 405–422. [CrossRef] [Google Scholar]
  12. E. Burman and L. Oksanen, Data assimilation for the heat equation using stabilized finite element methods. Numer. Math. 139 (2018) 505–528. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  13. J.A. Burns, E.M. Cliff and C.N. Rautenberg, A distributed parameter control approach to optimal filtering and smoothing with mobile sensor networks, In 17th Mediterranean Conference on Control and Automation (2009), pp. 181–186. [Google Scholar]
  14. J.A. Burns and C.N. Rautenberg, Solutions and approximations to the Riccati integral equation with values in a space of compact operators. SIAM J. Control Optim. 53 (2015) 2846–2877. [CrossRef] [MathSciNet] [Google Scholar]
  15. J.A. Burns and C.N. Rautenberg, The infinite-dimensional optimal filtering problem with mobile and stationary sensor networks. Numer. Funct. Anal. Optim. 36 (2015) 181–224. [CrossRef] [MathSciNet] [Google Scholar]
  16. 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. (2012). [Google Scholar]
  17. D. Chapelle, A. Gariah, P. Moireau and J. Sainte-Marie, A Galerkin strategy with proper orthogonal decomposition for parameter-dependent problems - analysis, assessments and applications to parameter estimation. ESAIM: Math. Model. Numer. Anal. 47 (2013) 1821–1843. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  18. G. Chavent, Nonlinear Least Squares for Inverse Problems. Springer (2010). [Google Scholar]
  19. R.F. Curtain, A survey of infinite-dimensional filtering. SIAM Rev. 17 (1975) 395–411. [CrossRef] [MathSciNet] [Google Scholar]
  20. R.F. Curtain, K. Mikkola and A. Sasane, The Hilbert-Schmidt property of feedback operators. J. Math. Anal. Appl. 329 (2007) 1145–1160. [CrossRef] [MathSciNet] [Google Scholar]
  21. R.F. Curtain and H. Zwart, An introduction to infinite-dimensional linear systems theory. Vol. 21 of Texts in Applied Mathematics. Springer-Verlag, New York (1995). [CrossRef] [Google Scholar]
  22. S. De Marchi and M. Vianello, Peano’s kernel theorem for vector-valued functions and some applications. Numer. Funct. Anal. Optim. 17 (1996) 57–64. [CrossRef] [MathSciNet] [Google Scholar]
  23. H.W. Engl, M. Hanke and A. Neubauer, Regularization of inverse problems. Vol. 375 of Mathematics and its Applications. Kluwer Academic Publishers Group, Dordrecht (1996). [Google Scholar]
  24. F. Flandoli, On the semigroup approach to stochastic evolution equations. Stoch. Anal. Appl. 10 (1992) 181–203. [CrossRef] [Google Scholar]
  25. H. Fujita, N. Saito and T. Suzuki, Operator Theory and Numerical Methods, Studies in Mathematics and Its Applications. North Holland (2001). [Google Scholar]
  26. A. Germani, L. Jetto and M. Piccioni, Galerkin approximation for optimal linear filtering of infinite-dimensional linear systems. SIAM J. Control Optim. 26 (1988) 1287–1305. [CrossRef] [MathSciNet] [Google Scholar]
  27. L. Grasedyck, W. Hackbusch and B.N. Khoromskij, Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices. Comput. Arch. Sci. Comput. 70 (2003) 121–165. [Google Scholar]
  28. S. Guerrero and G. Lebeau, Singular optimal control for a transport-diffusion equation. Commun. Partial Differ. Equ. 32 (2007) 1813–1836. [CrossRef] [Google Scholar]
  29. W. Hackbusch, A sparse matrix arithmetic based on H-matrices. I. Introduction to H-matrices. Comput. Arch. Sci. Comput. 62 (1999) 89–108. [Google Scholar]
  30. W. Hackbusch, Hierarchical Matrices: Algorithms and Analysis, Springer Publishing Company, Incorporated, 1st edition (2015). [Google Scholar]
  31. R.E. Kalman, A new approach to linear filtering and prediction problems. J. Basic Eng. 82 (1960) 35–45. [CrossRef] [Google Scholar]
  32. R.E. Kalman and R.S. Bucy, New results in linear filtering and prediction theory. J. Basic Eng. 83 (1961) 95–108. [CrossRef] [Google Scholar]
  33. T. Kato, Fractional powers of dissipative operators. J. Math. Soc. Jpn. 13 (1961) 246–274. [CrossRef] [Google Scholar]
  34. I. Lasiecka and R. Triggiani, Differential and Algebraic Riccati Equations with Application to Boundary/Point Control Problems: Continuous Theory and Approximation Theory. Lecture Notes in Control and Information Sciences. Springer, Berlin, Heidelberg (1991). [CrossRef] [Google Scholar]
  35. C. Le Bris and P. Rouchon, Low-rank numerical approximations for high-dimensional Lindblad equations. Phys. Rev. A 87 (2013) 022125. [CrossRef] [Google Scholar]
  36. F.-X. Le Dimet, Optimal control for data assimilation in meteorology, In Control theory of distributed parameter systems and applications (Shanghai, 1990). Vol. 159 of Lecture Notes in Control and Inform. Sci. Springer, Berlin (1991), pp. 51–60. [Google Scholar]
  37. F.-X. Le Dimet and O. Talagrand, Variational algorithms for analysis and assimilation of meteorological observation: theoretical aspects. Tellus 38 (1986) 97–110. [CrossRef] [Google Scholar]
  38. J.Y. Li, S. Ambikasaran, E.F. Darve and P.K. Kitanidis, A Kalman filter powered by H2-matrices for quasi-continuous data assimilation problems. Water Resour. Res. 50 (2014) 3734–3749. [CrossRef] [Google Scholar]
  39. J.-L. Lions, Controle optimal de systèmes gouvernés par des équations aux dérivées partielles, Avant propos de P. Lelong. Dunod, Paris (1968). [Google Scholar]
  40. J.-L. Lions, Exact controllability, stabilization and perturbations for distributed systems. SIAM Rev. 30 (1988) 1–68. [Google Scholar]
  41. J.-L. Lions, Espaces d’interpolation et domaines de puissances fractionnaires d’opérateurs. J. Math. Soc. Jpn. 14 (1962) 233–241. [CrossRef] [Google Scholar]
  42. Y. Maday, A.T. Patera, J.D. Penn and M. Yano, A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics. Int. J. Numer. Methods Eng. 102 (2014) 933–965. [Google Scholar]
  43. A. Nassiopoulos and F. Bourquin, Fast three-dimensional temperature reconstruction. Comput. Methods Appl. Mech. Eng. 199 (2010) 3169–3178. [CrossRef] [Google Scholar]
  44. S. Pagani, A. Manzoni and A. Quarteroni, Efficient state/parameter estimation in nonlinear unsteady PDEs by a reduced basis ensemble Kalman filter. SIAM/ASA J. Uncert. Quantif. 5 (2017) 890–921. [CrossRef] [Google Scholar]
  45. A. Pazy, Semigroups of linear operators and applications to partial differential equations. Vol. 44 of Applied Mathematical Sciences. Springer-Verlag, New York (1983). [CrossRef] [Google Scholar]
  46. D.T. Pham, J. Verron and M.C. Roubaud, A singular evolutive extended Kalman filter for data assimilation in oceanography. J. Mar. Syst. 16 (1998) 323–340. [CrossRef] [Google Scholar]
  47. S. Sellam and A. Forcioli, Introduction de la notion d’écart entre sous-espaces vectoriels en analyse de données. RAIRO: Oper. Res. 14 (1980). [Google Scholar]
  48. D. Simon, Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches. Wiley-Interscience (2006). [Google Scholar]
  49. H. Tanabe, Equations of evolution. Vol. 6 of Monographs and Studies in Mathematics, Pitman (Advanced Publishing Program), Boston, Mass.-London (1979). [Google Scholar]
  50. R. Temam, Sur l’équation de Riccati associée à des opérateurs non bornés, en dimension infinie. J. Funct. Anal. 7 (1971) 85–115. [CrossRef] [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.