Finite-time stabilization of 2 x 2 hyperbolic systems on tree-shaped networks

Abstract : We investigate the finite-time boundary stabilization of a one-dimensional 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.
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Article dans une revue
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2014, 52 (1), pp.143--163
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https://hal-mines-paristech.archives-ouvertes.fr/hal-01112021
Contributeur : François Chaplais <>
Soumis le : lundi 2 février 2015 - 10:11:35
Dernière modification le : lundi 12 novembre 2018 - 11:05:26

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  • HAL Id : hal-01112021, version 1

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Vincent Perrolaz, Lionel Rosier. Finite-time stabilization of 2 x 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-01112021〉

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