Optimal Control of Sediment Deposition in Shallow Waters - Sore, Seydou; Simpore, Yacouba (Optimal Control Applications & Methods, 2025)
This article presents an algebraic method for designing an initial bed profile to ensure minimal sediment deposition in open channels. We address the hyperbolic system of partial differential equations, known as the Saint-Venant-Exner system, which describes the behavior of water flow and sediment transport. By applying a priori estimation techniques and reformulating the problem as an optimal control problem, we construct a minimizing control law, via the adjoint method. This control law ensures the stability of the system and minimizes sediment deposition. In addition, a finite volume scheme is implemented to numerically solve both the direct system (SVE) and its adjoint system. Numerical simulations are provided for illustration. In theses simulations, an experimental rectangular channel with a unit width and a length 100m was considered. First, based on the control result, a bed profile that minimizes sediment deposition while simultaneously stabilizing the system's state was identified. Then, additional simulations were conducted to illustrate the sensitivity of the control solution to variations in sediment parameters and to the initial conditions.
CRIS-Team Scopus Importer:2025-03-21
Keywords: initial bed profile detection; optimal control; Saint-Venant-Exner model; sediment transport