Boundary feedback stabilization of hydraulic jumps

Georges Bastin; Jean Michel Coron; Amaury Hayat; Peipei Shang

doi:10.1016/j.ifacsc.2019.100026

Boundary feedback stabilization of hydraulic jumps

Georges Bastin
, Jean Michel Coron
, Amaury Hayat
, Peipei Shang

Department of Mathematical Engineering
University of Louvain
Université Paris-Diderot SPC
Sorbonne Université
School of Mathematical Sciences
Tongji University

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

In an open channel, a hydraulic jump is an abrupt transition between a torrential (supercritical) flow and a fluvial (subcritical) flow. In this article hydraulic jumps are represented by discontinuous shock solutions of hyperbolic Saint-Venant equations. Using a Lyapunov approach, we prove that we can stabilize the state of the system in H²-norm as well as the hydraulic jump location, with simple feedback boundary controls and an arbitrary decay rate, by appropriately choosing the gains of the feedback boundary controls.

Original language	English
Pages (from-to)	100026
Number of pages	1
Journal	IFAC Journal of Systems and Control
Volume	7
DOIs	https://doi.org/10.1016/j.ifacsc.2019.100026
Publication status	Published - 30 Mar 2019

Keywords

Boundary feedback controls
Hydraulic jump
Saint-Venant equations

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10.1016/j.ifacsc.2019.100026

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abstract = "In an open channel, a hydraulic jump is an abrupt transition between a torrential (supercritical) flow and a fluvial (subcritical) flow. In this article hydraulic jumps are represented by discontinuous shock solutions of hyperbolic Saint-Venant equations. Using a Lyapunov approach, we prove that we can stabilize the state of the system in H2-norm as well as the hydraulic jump location, with simple feedback boundary controls and an arbitrary decay rate, by appropriately choosing the gains of the feedback boundary controls.",

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author = "Georges Bastin and Coron, \{Jean Michel\} and Amaury Hayat and Peipei Shang",

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AU - Bastin, Georges

AU - Coron, Jean Michel

AU - Hayat, Amaury

AU - Shang, Peipei

PY - 2019/3/30

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N2 - In an open channel, a hydraulic jump is an abrupt transition between a torrential (supercritical) flow and a fluvial (subcritical) flow. In this article hydraulic jumps are represented by discontinuous shock solutions of hyperbolic Saint-Venant equations. Using a Lyapunov approach, we prove that we can stabilize the state of the system in H2-norm as well as the hydraulic jump location, with simple feedback boundary controls and an arbitrary decay rate, by appropriately choosing the gains of the feedback boundary controls.

AB - In an open channel, a hydraulic jump is an abrupt transition between a torrential (supercritical) flow and a fluvial (subcritical) flow. In this article hydraulic jumps are represented by discontinuous shock solutions of hyperbolic Saint-Venant equations. Using a Lyapunov approach, we prove that we can stabilize the state of the system in H2-norm as well as the hydraulic jump location, with simple feedback boundary controls and an arbitrary decay rate, by appropriately choosing the gains of the feedback boundary controls.

KW - Boundary feedback controls

KW - Hydraulic jump

KW - Saint-Venant equations

UR - https://www.scopus.com/pages/publications/85077462948

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DO - 10.1016/j.ifacsc.2019.100026

M3 - Article

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SN - 2468-6018

VL - 7

SP - 100026

JO - IFAC Journal of Systems and Control

JF - IFAC Journal of Systems and Control

ER -

Boundary feedback stabilization of hydraulic jumps

Abstract

Keywords

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