Minimal time for the exact controllability of one-dimensional first-order linear hyperbolic systems by one-sided boundary controls

Long Hu (1) , Guillaume Olive (2)

1 INSTITUTE OF MATHEMATICS - Shandong Universtity
2 Institute of Mathematics Jagiellonian University

In this article we study the minimal time for the exact controllability of one-dimensional first-order linear hyperbolic systems when all the controls are acting on the same side of the boundary. We establish an explicit and easy-to-compute formula for this time with respect to all the coupling parameters of the system. This partially solves an open problem raised in the celebrated survey [Rus78] and in the article [Hu15]. The proof relies on the introduction of a canonical UL-decomposition and the compactness-uniqueness method.

Mots clés: Hyperbolic systems; Minimal control time; Boundary controllability; UL-decomposition; Compactness-uniqueness method

Domaines: Optimisation et contrôle [math.OC]

Long Hu, Guillaume Olive. Minimal time for the exact controllability of one-dimensional first-order linear hyperbolic systems by one-sided boundary controls. 2019. ⟨hal-01982662v1⟩