Switching controls for analytic semigroups and applications to parabolic systems

Felipe W. Chaves Silva (1) , Sylvain Ervedoza (2) , Diego Araujo de Souza (3)

1 UFPB - Universidade Federal da Paraiba / Federal University of Paraiba
2 IMB - Institut de Mathématiques de Bordeaux
3 Federal University of Pernambuco [Recife]

In this work, we push further the analysis of the problem of switching controls proposed in [31]. The problem consists in the following one: assuming that one can control a system using two or more actuators, does there exist a control strategy such that at all times, only one actuator is active? We answer positively to this question when the controlled system corresponds to an analytic semigroup spanned by a positive self-adjoint operator which is null-controllable in arbitrary small times. Similarly as in [31], our proof relies on analyticity arguments and will also work in finite dimensional setting and under some further spectral assumptions when the operator spans an analytic semigroup but is not necessarily self-adjoint.

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

Felipe W. Chaves Silva, Sylvain Ervedoza, Diego Araujo de Souza. Switching controls for analytic semigroups and applications to parabolic systems. 2020. ⟨hal-03001962v1⟩