Stochastic model predictive control based on Gaussian processes applied to drinking water networks

Abstract

This paper focuses on developing a stochastic model predictive control (MPC) strategy based on Gaussian Processes (GPs) for propagating system disturbances in a receding horizon way. Using a probabilistic system representation, the state trajectories considering the influence of disturbances can be obtained through the uncertainty propagation by using GPs. This fact allows obtaining the confidence intervals for state evolutions over the MPC prediction horizon that are included into the MPC objective function and constraints. The feasibility of the proposed MPC strategy considering the incorporated results of disturbance forecasting is also discussed. Simulation results obtained from the application of the proposed approach to the Barcelona drinking water network (DWN) taking real demand data into account are presented.The comparison with the well-known certainty-equivalent MPC shows the effectiveness of the proposed stochastic MPC approach.

Non-linear economic model predictive control of water distribution networks

“…Therefore, these constraints should complement the mass balance principles and physical relations between flow and head introduced in (13). In the following, these 240 physical constraints are described in detail.…”

“…Related research for WDNs has been carried out in the past several years [6,7,8,9,10,11,12,13,14,15]. These research works are focused on finding the optimal operation on 35 the WDN in order to achieve the desired control objectives.…”

“…For this purpose, some optimal control problems are posed and solved to minimise the total operational costs of WDNs, for instance in [6,16] the genetic algorithm (GA) is chosen. In [7,8,10,13], authors have successfully applied the MPC strategy in the WDN using a control-oriented model that considers only flows, i.e., the pressure/head model of each element in the WDN including 40 water storage tanks/reservoirs, water demand sectors, pressurised pipes, booster pumps and pressure/flow-controlled valves, are not considered explicitly. For a certain WDN, in addition to satisfy water demands, it is also necessary to meet the required pressure/head at each water demand sector and particular control points.…”

Optimal Management of Barcelona Water Distribution Network using Non-linear Model Predictive Control

“…MPC is quite suitable to be used in the global control of networks related to the urban water cycle within a hierarchical control structure (Ocampo-Martinez et al, 2013). However, in Ocampo-Martinez et al (2013); Grosso et al (2014); Wang et al (2015Wang et al ( , 2016a, MPC strategy was successfully applied to the WDN using a control-oriented model that considers only flows, i.e., the pressure/head model of each element in the WDN (including water storage tanks/reservoirs, water demand sectors, pressurised pipes, booster pumps and pressure/flow-controlled valves) is not considered explicitly. But, for general WDN, in order to satisfy water demands, it is also necessary to meet the required pressure/head at each water demand sector, which implies adding a set of non-linear constraints to the optimisation problem.…”

Periodic Nonlinear Economic Model Predictive Control with Changing Horizon for Water Distribution Networks

“…(Brdys and Ulanicki, 1994;Cembrano et al, 2000;OcampoMartinez et al, 2013;Wang et al, 2016a). In these references, the optimal flow set-points for actuators (pumps and valves) can be computed by solving a finite-horizon optimization problem with the minimization of a multiobjective problem including economic costs and safety This work has been partially funded by the Spanish Government and FEDER through the projects CICYT ECOCIS (ref.…”