Abstract
We consider in this article a filtering problem for a linear distributed parameter system where the input disturbances are located in points instead of being distributed. The observation process is assumed to be distributed inside the domain. Although formally one can derive equations for the Kalman filter and the Riccati equation, the complete justification of these equations leads to problems which cannot be solved by standard methods, in the sense that some new functional spaces need to be introduced. The objective of the paper is to give a rigorous treatment of this nonclassical filtering problem, which is relevant for applications.
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A. Bensoussan,Filtrage Optimal des Systèmes Linéaires, Dunod: Paris, 1971.
A. Bensoussan, M. Delfour, S. K. Mitter,Infinite Dimensional System Theory, MIT Press: Boston (to be published).
J.-L. Lions, Lectures at College de France: , 1979.
J.-L. Lions, E. Magenes,Problèmes aux Limites non Homogènes et Applications, vols. I & II, Dunod-Gauthier Villars: Paris, 1968; Eng. tr., Springer-Verlag: New York, 1970.
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Communicated by J.-L. Lions
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Bensoussan, A., Lions, J.L. Filtering of distributed parameter systems with pointwise disturbances. Appl Math Optim 7, 191–224 (1981). https://doi.org/10.1007/BF01442116
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DOI: https://doi.org/10.1007/BF01442116