Abstract:

This thesis is devoted to developing a robust Model Predictive Control (MPC) strategy based
on Gaussian Processes (GP), especially for Drinking Water Networks (DWN). Nowadays there
are many different MPC strategies developed for DWN, such as certainequivalent MPC (CEMPC)
and chanceconstrained MPC (CCMPC). The general control objectives for DWN are
economic by managing the water supply to minimise water production and transport costs, all
the tanks running in safe ways with their limitations and reducing the undesired abrupt changes
by minimising their slew rate and obtaining smooth signals. For the deterministic system model,
the control objectives are elementary fulfilled. But the main challenge for DWN is to propagate
and incorporate exogenous and endogenous uncertainties to MPC closed loop over the prediction
horizon. Considering the controloriented model of the DWN, the MPC controller design
is hereby divided into two parts: system disturbances forecasting and the robust MPC controller
design. Case studies based on Barcelona DWN have been executed to verify the performance
of proposed methodologies.
The first part of this thesis leads to forecast system disturbances by using GP. In a DWN system,
system disturbances come mainly water demands associated to consumer sectors. Hence,
it is necessary to model each water demand and forecast the water demand in a short term that
covers the MPC prediction horizon. GP regression is regarded as one of stateoftheart regression
methods able to select model parameters by using Bayesian Inference theory with a
collection of past data. Besides, it is believed that the GP regression method has a difficult for
the multiplestep ahead forecasting. Hence, the Doubleseasonal Holtwinters method is used
for forecasting the expected disturbances while the stochastic disturbances are forecasted by using
GP. Finally, the desired forecasting results are a set of Gaussian distributions over the MPC
prediction horizon.
The second part of this thesis is to incorporate the forecasting results from GP within MPC
closed loop. This MPC strategy based on GP is named GPMPC. Using the given system model,
the deterministic state evolutions can be obtained while the uncertainty of state propagation over a given prediction horizon can be also achieved though the linear approximation of GP. Therefore,
the worstcase state evolutions over the MPC prediction horizon can also be determined
in the MPC cost function and constraints. The desired performance of applying GPMPC in
the closedloop system is that the system has more safety than the CEMPC and meanwhile it
probably brings more expenses.
Comparisons of GPMPC and previous developed approaches are carried out by a case study
of the threetank system inspired in the Barcelona DWN. A set of key performance indicators are
defined to compare performances of different MPC strategies. Finally, through the simulation
results, the GPMPC has the similar performance as the CCMPC, both of which have much
more expenses than the CEMPC. As a result of considering the uncertainties inside the system,
more expenses is necessary to maintain the safety of the whole system. Hence, the GPMPC
is more advanced. Moreover, the proposed GPMPC is required to be tested with the whole
DWN and using the real data from a DWN system. So the future works of this thesis have been
outlined. 