Finite-time boundary stabilization of general linear hyperbolic balance laws via Fredholm backstepping transformation

Jean-Michel Coron (1) , Long Hu (2) , Guillaume Olive (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 School of Mathematics [Shandong]
3 IMB - Institut de Mathématiques de Bordeaux

This paper is devoted to a simple and new proof on the optimal finite control time for general linear coupled hyperbolic system by using boundary feedback on one side. The feedback control law is designed by first using a Volterra transformation of the second kind and then using an invertible Fredholm transformation. Both existence and invertibility of the transformations are easily obtained.

Mots clés: Boundary stabilization; Coupled hyperbolic systems; Optimal finite time; Fredholm transformation

Domaines: Optimisation et contrôle [math.OC]

Jean-Michel Coron, Long Hu, Guillaume Olive. Finite-time boundary stabilization of general linear hyperbolic balance laws via Fredholm backstepping transformation. Automatica, 2017, 84, ⟨10.1016/j.automatica.2017.05.013⟩. ⟨hal-01437107⟩