Model Predictive Control in Urban Systems

This dissertation is about Model Predictive Control (MPC) and its application to sewer networks. Our main interest is to control sewer networks, such that the wastewater is kept inside the network and not overowing into the nearby environments, if possible. Towards this goal, we consider the use of the predictive abilities of MPC, an optimal control method, to account for the coming rain inow to the network; provided through known forecasts. An outline of the physics of sewer networks is presented, such as the SaintVenant equations and overows from weirs, including an outline of the general goals for the operation of the network. An outline is given for dierent approaches to formulating design models for the control of the sewer. We show dierent methods of how overow from weirs can be included in MPC for linear designs, and discuss the benets of each approach For more realistic scenarios, we assume the presence of uncertainty in the rain forecasts applied to the MPC. We outline dierent approaches to MPC with handling of uncertainty; such as tube-based MPC and Chance-constrained
MPC(CC-MPC). We show how the probabilistic formulation of CC-MPC can be adapted to handle the presence of weirs; by the addition of constraints for
dening the expected overows, and probabilistic constraints on the avoidment of overow. A discussion on the dierent approaches to uncertainty is given;
showing how similar and dierent they are. We outline how the stochastic distributions of the constraints utilized by CC-MPC can be estimated, based on the usage of ensemble forecasts. We show how the estimation can be applied to CC-MPC, to obtain computational simpler optimization programs.