  Control of water distribution networks (WDNs) can be represented by an
optimization problem with hydraulic models describing the nonlinear
relationship between head loss, water flow, and demand. The problem is
difficult to solve due to the non-convexity in the equations governing water
flow. Previous methods used to obtain WDN controls (i.e., operational schedules
for pumps and valves) have adopted simplified hydraulic models. One common
assumption found in the literature is the modification of WDN topology to
exclude loops and assume a known water flow direction. In this paper, we
present a new geometric programming-based model predictive control approach,
designed to solve the water flow equations and obtain WDN controls. The paper
considers the nonlinear difference algebraic equation (DAE) form of the WDN
dynamics, and the GP approach amounts to solving a series of convex
optimization problems and requires neither the knowledge of water flow
direction nor does it restrict the water network topology. A case study is
presented to illustrate the performance of the proposed method.
