Optimal monitoring and management of a water storage with pollution constraints

The aim is to fill water storage with potable water of a given quality, for subsequent treatment and distribution to a water conveying system. During a given period, a set of several pumping stations is working to deliver water from different sources at different locations. A multi-stage control process is considered whereby the total pumping time is divided into short sampling intervals. The intensity of pumping as a function of time is the control variable. It is assumed that there exists a reliable forecast of every pollutant as a function of time and water source. The amount of the pollutants is constrained in the final mass of water in the storage. The mass of water at the end of the operation period should be maximized