English

Finite-Time Stabilization Of Systems Of Conservation Laws On Networks

Analysis of PDEs 2013-02-26 v1

Abstract

We investigate the finite-time boundary stabilization of a 1-D first order quasilinear hyperbolic system of diagonal form on [0,1]. The dynamics of both boundary controls are governed by a finite-time stable ODE. The solutions of the closed-loop system issuing from small initial data in Lip([0,1]) are shown to exist for all times and to reach the null equilibrium state in finite time. When only one boundary feedback law is available, a finite-time stabilization is shown to occur roughly in a twice longer time. The above feedback strategy is then applied to the Saint-Venant system for the regulation of water flows in a network of canals.

Keywords

Cite

@article{arxiv.1302.5812,
  title  = {Finite-Time Stabilization Of Systems Of Conservation Laws On Networks},
  author = {Vincent Perrollaz and Lionel Rosier},
  journal= {arXiv preprint arXiv:1302.5812},
  year   = {2013}
}