Compact perturbations of controlled systems

Michel Duprez (1) , Guillaume Olive (2)

1 I2M - Institut de Mathématiques de Marseille
2 IMB - Institut de Mathématiques de Bordeaux

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.

Mots clés: Compactness-uniqueness; Fattorini-Hautus test; Exact controllability; Reachable states

Domaines: Optimisation et contrôle [math.OC]; Analyse fonctionnelle [math.FA]; Equations aux dérivées partielles [math.AP]

Michel Duprez, Guillaume Olive. Compact perturbations of controlled systems. Mathematical Control and Related Fields, 2018, 8 (2), pp.397-410. ⟨hal-01406540v2⟩