Robust Model Predictive Control based on Gaussian Processes: Application to drinking water networks

In this paper, a controller design based on robust Model Predictive Control (MPC) and Gaussian Processes (GP) for incorporating the disturbance forecasting has been proposed. Using a probabilistic system representation, the state trajectories considering the influence of disturbances can be obtained through the uncertainty propagation by using GP. Therefore, the worst-case state trajectories evolution over the MPC prediction horizon can be determined, which are potentially used by including them into the MPC cost function and constraints. For the purpose of inspecting the performance of proposed controller, it has been compared with a certain-equivalent MPC and a chance-constrained MPC. Results of the application the proposed approach to Barcelona Drinking Water Network (DWN) have shown the effectiveness of the approach and comparison results with the other considered MPC approaches have shown the advantages and drawbacks of each approach.