Stochastic Model Predictive Control based on Gaussian Processes applied to Drinking Water Networks

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. Index Terms Stochastic Model Predictive Control, Gaussian Processes, Disturbance Forecasting, Drinking Water Networks.