Decentralized control of a water distribution network using Repeated Games

In this paper, our aim is to design a decentralized control scheme for pumping stations in a water distribution network that supplies drinking water. The considered water distribution network consists only of pumping stations, piping networks, and consumers (since the inclusion of storage tanks poses the risk of contamination of drinking water). The pumping stations supply water to consumers and their objective is to ensure the supply of water to the consumers in an optimal way such that the consumer demand is satisfied with minimum energy consumption by the pumping station itself. This gives rise to a non-zero-sum game as the pumping stations have a common objective of satisfying consumer demand and a selfish objective of minimizing their own energy consumption. A real-life water distribution network with two pumping stations was emulated in a lab and the proposed control scheme was tested on this setup. The consumer demand follows a periodic trend that mimics real-life consumption and has some stochastic noise added to it so as to emulate uncertainty in consumer demand. The proposed control scheme was able to track the reference signal while each pumping station was minimizing its own energy consumption.