Recovering the observable part of the initial data of an infinite-dimensional linear system with skew-adjoint generatorReport as inadecuate




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1 DMIA - Département de Mathématiques, Informatique, Automatique

Abstract : We consider the problem of recovering the initial data or initial state of infinite-dimensional linear systems with unitary semigroups. It is well-known that this inverse problem is well posed if the system is exactly observable, but this assumption may be very restrictive in some applications. In this paper we are interested in systems which are not exactly observable, and in particular, where we cannot expect a full reconstruction. We propose to use the algorithm studied by Ramdani et al. in Automatica 46:1616-1625, 2010 and prove that it always converges towards the observable part of the initial state. We give necessary and sufficient condition to have an exponential rate of convergence. Numerical simulations are presented to illustratethe theoretical results.

Keywords : Linear systems Inverse problems Controllability Observability Feedback control





Author: Ghislain Haine -

Source: https://hal.archives-ouvertes.fr/



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