3IECL - Institut Élie Cartan de Lorraine (Université de Lorraine, Boulevard des Aiguillettes BP 70239 54506 Vandoeuvre-les-Nancy Cedex
Ile du Saulcy - 57 045 Metz Cedex 01 - France)
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.
https://hal.archives-ouvertes.fr/hal-00793728
Contributeur : Lionel Rosier
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Soumis le : vendredi 22 février 2013 - 19:22:32
Dernière modification le : lundi 12 novembre 2018 - 11:05:27
Document(s) archivé(s) le : dimanche 2 avril 2017 - 04:37:04
Vincent Perrollaz, Lionel Rosier. Finite-time stabilization of 2*2 hyperbolic systems on tree-shaped networks. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2014, 52 (1), pp.143-163. 〈hal-00793728〉
