Nonnegative boundary control of 1D linear heat equations

Jérôme Lohéac (1)

1 CRAN - Centre de Recherche en Automatique de Nancy

We consider the controllability of a one dimensional heat equation with nonnegative boundary controls. Despite the controllability in any positive time of this system, the unilateral nonnegativity control constraint causes a positive minimal controllability time. In this article, it is proved that at the minimal time, there exists a nonnegative control in the space of Radon measures, which consists of a countable sum of Dirac impulses.

Mots clés: Minimal time; Nonnegative control; Dirac impulse; 1D heat equation

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

Jérôme Lohéac. Nonnegative boundary control of 1D linear heat equations. Vietnam Journal of Mathematics, 2021, 49 (3), pp.845-870. ⟨10.1007/s10013-021-00497-5⟩. ⟨hal-02613883v2⟩