This paper addresses a non-linear economic model predictive control (EMPC) strategy for water distribution networks (WDNs). A WDN could be considered as a non-linear system described by differential-algebraic equations (DAEs) when flow and hydraulic head equations are considered. As in other process industries, the main operational goal of WDNs is the minimisation of the economic costs associated to pumping and water treatment, while guaranteeing water supply with required flows and pressures at all the control/demand nodes in the network. Other operational goals related to safety and reliability are usually sought. From a control point of view, EMPC is a suitable control strategy for WDNs since the optimal operation of the network cannot be established a priori by fixing reference volumes in the tanks. Alternatively, the EMPC strategy should determine the optimal filling/emptying sequence of the tanks taking into account that electricity price varies between day and night and that the demand also follows a 24-hour repetitive pattern. On the other hand, as a result of the ON/OFF operation of parallel pumps in pumping stations, a two-layer control scheme has been used: a non-linear EMPC strategy with hourly control interval is chosen in the upper layer and a pump scheduling approach with one-minute sampling time in the lower layer. Finally, closed-loop simulation results of applying the proposed control strategy to the D-Town water network are shown.
In this paper, a periodic economic model predictive control (EMPC) strategy with nonlinear algebraic
constraint relaxations for water distribution networks (WDNs) is presented. A WDN is usually modeled by a series
of differential-algebraic equations. When the hydraulic pressure/head and flow relations in the interconnected pipes
are considered, the nonlinear algebraic equations will appear in the control-oriented model of WDNs. Specifically,
two types of nonlinear algebraic equations are studied in terms of unidirectional and bidirectional flows in pipes.
These nonlinear algebraic constraints are iteratively relaxed by a series of linear constraints. Therefore, the proposed
EMPC strategy can be implemented by solving an optimization problem using the linear programming technique.
Finally, the EMPC strategy with nonlinear algebraic constraint relaxations is verified in the Richmond water network.
The comparison results of applying nonlinear EMPC strategy are also provided. The proposed nonlinear-constraint
relaxation technique turns out to be much faster than the one obtained by a standard nonlinear optimization solver.
This study 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 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.
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 certainequivalent 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.