Compact perturbations of controlled systems

Michel Duprez; Guillaume Olive

doi:10.3934/mcrf.2018016

Article Contents

2018, Volume 8, Issue 2: 397-410. Doi: 10.3934/mcrf.2018016

This issue Previous Article Asymptotic behavior of a Schrödinger equation under a constrained boundary feedback Next Article Finite element error analysis for measure-valued optimal control problems governed by a 1D wave equation with variable coefficients

Compact perturbations of controlled systems

Michel Duprez^1, and
Guillaume Olive^2, ,

1.
Institut de Mathématique de Marseille, Aix Marseille Université, 39, rue J. Joliot Curie, 13453 Marseille Cedex 13, France
2.
Institut de Mathématiques de Bordeaux, Université de Bordeaux, 351, Cours de la Libération, 33405 Talence, France

* Corresponding author: Guillaume Olive
* Corresponding author: Guillaume Olive

Received: December 2016

Revised: February 2018

Published: June 2018

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Abstract

In this article we study the controllability properties of general compactly perturbed exactly controlled linear systems with admissible control operators. Firstly, we show that approximate and exact controllability are equivalent properties for such systems. Then, and more importantly, we provide for the perturbed system a complete characterization of the set of reachable states in terms of the Fattorini-Hautus test. The results rely on the Peetre lemma.

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Mathematics Subject Classification: Primary: 93B05, 93C73; Secondary: 93C73.

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References

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