Internal rapid stabilization of a linear transport equation with a scalar feedback
Abstract
We use a variant of the backstepping method to study the stabilization of a 1-D linear transport equation on the interval (0,L), by controlling the scalar amplitude of a piecewise regular function of the space variable in the source term. We prove that if the system is controllable in a periodic Sobolev space of order greater than 1, then the system can be stabilized exponentially in that space and, for any given decay rate, we give an explicit feedback law that achieves that decay rate. The variant of the backstepping method used here relies mainly on the spectral properties of the linear transport equation, and leads to some original technical developments that differ substantially from previous applications.
Type
Publication
Mathematical Control & Related Fields
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.