Modeling and control of in-situ decontamination of large water resources

Abstract

Abstract.We address the problem of the optimal control of in situ decontamination of water resources. We review several modeling, simulation and optimization techniques for this problem and their results. We show the benefit of combining tools from finite dimensional optimal control theory and numerical simulations of hydrodynamics equations, for providing simple and efficient feedback strategies.Résumé. Nous considérons le problème de commande optimale d'une décontamination in situ de ressources hydriques. Nous passons en revue différentes techniques de modélisation, simulation et optimisation pour ce problème, ainsi que leurs résultats. Nous montrons le bénéficeà combiner les outils de la théorie de la commande optimale en dimension finie avec la simulation numérique deś equations de l'hydrodynamique, afin de fournir des stratégies par retour d'étatà la fois simples et efficaces.

Controlling recirculation rate for minimal-time bioremediation of natural water resources

“…In [4], it has been proved the remarkable property that the expres-sion of the optimal feedback control is preserved when considering one (or more) "dead" areas in the modeling of heterogeneity of the pollutant concentration in water resources. This has led to a validation of this feedback control on realistic simulations of the hydrodynamics of the resource based on the Navier-Stokes equations [1,2], justifying then the derivation of optimal control laws from simple o.d.e. models, without requiring the precise knowledge of the heterogeneity.…”

Optimal discharge locations to refill hydric reservoirs with reused water - application to the jaunay lake case study

“…To grasp the multiple issues to ascertain the appropriate location for the reused water discharge, mathematical modelling is particularly adapted for describing the water quality under different system and meteorological conditions (ALAVANI et al, 2010;BARBIER et al, 2016;GAJARDO et al, 2017;RAPAPORT et al, 2014). Our strategy resides in introducing a mathematical model which describes the evolution of the water quality in the reservoir, carrying out numerical simulations and solving the desired optimization problem with an appropriate optimization algorithm.…”