Backstepping Stabilization of the Linearized Saint-Venant-Exner Model

Ababacar Diagne; Mamadou Diagne; Shuxia Tang; Miroslav Krstic

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arXiv · 1505.06367

Backstepping Stabilization of the Linearized Saint-Venant-Exner Model

Ababacar Diagne·Mamadou Diagne·Shuxia Tang·Miroslav Krstic

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Abstract

Using the backstepping design, we achieve exponential stabilization of the coupled Saint-Venant-Exner (SVE) PDE model of water dynamics in a sediment-filled canal with arbitrary values of canal bottom slope, friction, porosity, and water-sediment interaction under subcritical or supercritical flow regime. The studied SVE model consists of two rightward convecting transport Partial Differential Equations (PDEs) and one leftward convecting transport PDE. A single boundary input control (with actuation located only at downstream) strategy is adopted. A full state feedback controller is firstly designed, which guarantees the exponential stability of the closed-loop control system. Then, an output feedback controller is designed based on the reconstruction of the distributed state with a backstepping observer. It also guarantees the exponential stability of the closed-loop control system. The flow regime depends on the dimensionless Froude number Fr, and both our controllers can deal with the subcritical (Fr < 1) and supercritical (Fr > 1) flow regime. They achieve the exponential stability results without any restrictive conditions in contrast to existing results.

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BibTeX RIS

Ababacar Diagne, Mamadou Diagne, Shuxia Tang, Miroslav Krstic. 2015-05-23. Backstepping Stabilization of the Linearized Saint-Venant-Exner Model. https://arxiv.org/abs/1505.06367

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