Output controllability in a long-time horizon

Martin Lazar (1) , Jérôme Lohéac (2)

1 University of Dubrovnik
2 CRAN - Centre de Recherche en Automatique de Nancy

In this article we consider a linear finite dimensional system. Our aim is to design a control such that the output of the system reach a given target at a final time T > 0. This notion is known as output controllability. We extend this notion to the one of long-time output controllability. More precisely, we consider the question: is it possible to steer the output of the system to some prescribed value in time T > 0 and then keep the output of the system at this prescribed value for all times t > T ? We provide a necessary and sufficient condition for this property to hold. Once the condition is satisfied, one can apply a feedback control that keeps the average fixed during a given time period. We also address the L2 -norm optimality of such controls. We apply our results to (long-time) averaged control problems.

Mots clés: Controlled invariant subspace; Linear optimal control; Open-loop control systems; Averaged control; Output controllability

Domaines: Systèmes dynamiques [math.DS]; Optimisation et contrôle [math.OC]

Martin Lazar, Jérôme Lohéac. Output controllability in a long-time horizon. Automatica, 2020, 113, pp.108762. ⟨10.1016/j.automatica.2019.108762⟩. ⟨hal-01888043v2⟩