Boundary feedback control of linear hyperbolic systems: Application to the Saint-Venant–Exner equations

Christophe Prieur, Joseph J. Winkin

Research output: Contribution to journalArticle

Abstract

Distributed parameter systems modeled by hyperbolic partial differential equations are considered in this paper. The dynamic models include a source term and heterodirectional velocities. A boundary control problem is introduced and it is first shown that it is well-posed (in the sense of Tucsnak and Weiss), under appropriate assumptions coupling the boundary conditions and the source term. Then a sufficient exponential stability condition is derived using operator theory. This condition is written in terms of Linear Matrix Inequalities that are numerically tractable and that allow an optimization program. Connections with another classical stability condition are given. This approach is applied to the Saint-Venant–Exner equation describing the dynamics of the water level, of the water flow and of the sediment inside of a channel. The effect of the friction and of the slope are taken into account in the application model.

Original languageEnglish
Pages (from-to)44-51
Number of pages8
JournalAutomatica
Volume89
DOIs
Publication statusPublished - 1 Mar 2018

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Water levels
Asymptotic stability
Linear matrix inequalities
Partial differential equations
Feedback control
Dynamic models
Sediments
Boundary conditions
Friction
Water

Cite this

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Boundary feedback control of linear hyperbolic systems : Application to the Saint-Venant–Exner equations. / Prieur, Christophe; Winkin, Joseph J.

In: Automatica, Vol. 89, 01.03.2018, p. 44-51.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Boundary feedback control of linear hyperbolic systems

T2 - Application to the Saint-Venant–Exner equations

AU - Prieur, Christophe

AU - Winkin, Joseph J.

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