# Backstepping Stabilization of the Linearized Saint-Venant-Exner Model

arXiv: https://arxiv.org/abs/1505.06367 · HTML: https://mlsanity.com/paper/1505.06367/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2015.

## Built on by (most cited first, 1 of 1)

- [Backstepping Neural Operators for 2× 2 Hyperbolic PDEs](https://mlsanity.com/paper/2312.16762/) (2023)

## Abstract (arXiv)

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.