Nonnegative Boundary Control of 1D Linear Heat Equations

Abstract

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.