Boundary feedback stabilization of hydraulic jumps. (30th March 2019)

• Record Type: Journal Article
• Authors: Bastin, Georges; Coron, Jean-Michel; Hayat, Amaury; Shang, Peipei
• Is Part Of: IFAC journal of systems and control. Volume 7(2019)
• Publication Date: 2019-03-30
• Subjects: 93D15 -- 35L40 -- 35L67; Saint-Venant equations -- Boundary feedback controls -- Hydraulic jump; Automatic control -- Periodicals; Relay control systems -- Periodicals; Embedded computer systems -- Periodicals; Feedback control systems -- Periodicals; Artificial intelligence -- Periodicals; Artificial intelligence; Automatic control; Embedded computer systems; Feedback control systems; Relay control systems; Electronic journals; Periodicals; 629.89
• DOI: 10.1016/j.ifacsc.2019.100026
• Languages: English
• ISSNs: 2468-6018

Abstract

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 H 2 -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.