On the assessment of tree-based and chance-constrained predictive control approaches applied to drinking water networks

Abstract

Water systems are a challenging problem because of their size and exposure to uncertain influences such as the unknown demands or the meteorological phenomena. In this paper, two different stochastic programming approaches are assessed when controlling a drinking water network: chance-constrained model predictive control (CC-MPC) and tree-based model predictive control (TB-MPC). Under the former approach, the disturbances are modeled as stochastic variables with non-stationary uncertainty description, unbounded support and quasi concave probabilistic distribution. A deterministic equivalent of the related stochastic problem is formulated using Boole¿s inequality and a uniform allocation of risk. In the later approach, water demand is modelled as a disturbance rooted tree where branches are formed by the most probable evolutions of the demand. In both approaches, a model predictive controller is used to optimise the expectation of the operational cost of the disturbed system.