A population dynamics approach for the water distribution problem

The water distribution system (WDS) is composed of 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 achieve an adequate level of water in the distribution tanks, we need to dynamically control the flow. Here, we propose a population dynamics approach in order to control tanks, by allocating in them the maximum uniform volume. The feedback interconnected systems reach a stable equilibrium point for both approaches presented (i.e. replicator and supply dynamics), and more specific an asymptotically stable equilibrium point for the replicator dynamics case. The stability analysis uses some passivity concepts and classic Lyapunov theory for a closed-loop system that combines the population dynamics (controller), and the WDS (process). We show via simulations the operation under different scenarios.