Time optimal boundary controls for the heat equation

Sorin Micu (1) , Ionel Roventa (1) , Marius Tucsnak (2, 3)

1 UCV - Department of Mathematics
2 IECN - Institut Élie Cartan de Nancy
3 CORIDA - Robust control of infinite dimensional systems and applications

The fact that the time optimal controls for parabolic equations have the bang-bang property has been recently proved for controls distributed inside the considered domain. The aim of this article consists in showing that the boundary controls for the heat equation have the same property, at least in rectangular domains. The main result is proved by combining results and methods from traditionally distinct fields: the Lebeau-Robbiano strategy for null controllability and estimates of the controllability cost in small time for parabolic systems, on one side, and a Remez-type inequality for Müntz spaces and a generalization of Tur{á}n's inequality, on the other side.

Domaines: Optimisation et contrôle [math.OC]

Sorin Micu, Ionel Roventa, Marius Tucsnak. Time optimal boundary controls for the heat equation. 2011. ⟨hal-00639717v2⟩