Finite-time internal stabilization of a 1-D linear transport equation
Abstract
We consider a 1-D linear transport equation on the interval (0, L), with an internal scalar control. We prove that if the system is controllable in a periodic Sobolev space of order greater than 1, then the system can be stabilized in finite time, and we give an explicit feedback law.
Type
Publication
Systems & Control Letters
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.