2015/05/23 by Ababacar Diagne, Diagne, Ababacar, Mamadou Diagne +7 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #math.OC
paper · pdf · doi:10.48550/arxiv.1505.06367
16 pages, 19 figures, Submitted to Automatica
arxiv created 2015/05/23 · openalex publication_date 2015/05/23 · arxiv updated 2015/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.