Internal Controllability of Systems of Semilinear Coupled One-Dimensional Wave Equations with One Control
Abstract
We prove the internal controllability of some systems of two coupled wave equations in one space dimension, with one control, under certain conditions on the coupling. To do this we apply the ‘fictitious control method’ in two cases: general systems with a ’non-degenerate’ coupling, and a particular case where the coupling is ‘degenerate’, namely a cubic coupling. In the latter case, our proof requires to find nontrivial trajectories of the control system that go from 0 to 0. We build these trajectories by adapting (in 1 space dimension) a construction developed by Jean-Michel Coron, Sergio Guerrero and Lionel Rosier for the study of coupled parabolic systems.
Type
Publication
SIAM Journal on Control and Optimization
Authors
Christophe Zhang
(he/him)
researcher
I am currently in secondment at Inria Paris, as a researcher in the CAGE team. I work on control, stabilization and optimal control problems in infinite dimension (PDEs and evolution equation), with a particular focus on constrained control.
I have also dabbled in data-driven modelling and control, in particular methods involving the Koopman operator.
More recently, I have taken an interest in reachability analysis. I co-supervised the PhD thesis of Ivan Hasenohr with Camille Pouchol and Yannick Privat, during which we developed computer-assisted proofs of reachability and non-reachability.