Null controllability of heat equation with switching controls under Robin’s boundary condition

Abstract

In this paper, we consider the null controllability of 1-d heat equation endowed with Robin’s boundary conditions, when the operator − d 2 dx2 has positive eigenvalues and try to find sufficient conditions for building switching controls. In [1], the author developed a first analysis of this problem with Dirichlet’s boundary conditions and obtain sufficient conditions for switching controls. We firstly consider 1-d heat system endowed with two controls. Then we try to build switching control strategies guaranteeing that, at each instant of time, only one control is activated.