Analysis and control for the water distribution problem

The water distribution system (WDS) is composed by several elements, where flow control is one of the most important components needed in order to provide a satisfactory level of service. In order to advene an adequate level of water in the distribution tanks, we need to dynamically control the flow. Here, we propose a replicator dynamics approach in order to control tanks, by allocating in them the maximum uniform volume. The feedback interconnected systems reach an asymptotically stable equilibrium point for this approach. The stability analysis uses some passivity concepts and classic Lyapunov theory for a closed-loop system that combines the replicator dynamics (controller), and the WDS (process). We show the operation under different scenarios via simulations.