This paper addresses a chance-constrained model predictive control (CC-MPC) strategy for the management of drinking water networks (DWNs) based on a finite horizon stochastic optimisation problem with joint probabilistic (chance) constraints. In this approach, water demands are considered additive stochastic disturbances with non-stationary uncertainty description, unbounded support and known (or approximated) quasi-concave probabilistic distribution. A deterministic equivalent of the stochastic problem is formulated using Boole's inequality to decompose joint chance constraints into single chance constraints and by considering a uniform allocation of risk to bound these later constraints. The resultant deterministic-equivalent optimisation problem is suitable to be solved with tractable quadratic programming (QP) or second order cone programming (SOCP) algorithms. The reformulation allows to explicitly and easily propagate uncertainty over the prediction horizon, and leads to a cost-efficient management of risk that consists in a dynamic back-off to avoid frequent violation of constraints. Results

In this paper we consider periodic optimal operation of constrained periodic linear systems. We propose an economic model predictive controller based on a single layer that unites dynamic real time optimization and control. The proposed controller guarantees closed-loop convergence to the optimal periodic trajectory that minimizes the average operation cost for a given economic criterion. A-priori calculation of the optimal trajectory is not required and if the economic cost function is changed, recursive feasibility and convergence to the new periodic optimal trajectory is guaranteed. The results are demonstrated with two simulation examples, a four tank system, and a simplified model of a section of Barcelona's water distribution network.

Drinking Water Networks (DWN) are large-scale multiple-input multiple-output systems with uncertain disturbances (such as the water demand from the consumers) and involve components of linear, non-linear and switching nature. Operating, safety and quality constraints deem it important for the state and the input of such systems to be constrained into a given domain. Moreover, DWNs' operation is driven by time-varying demands and involves an considerable consumption of electric energy and the exploitation of limited water resources. Hence, the management of these networks must be carried out optimally with respect to the use of available resources and infrastructure, whilst satisfying high service levels for the drinking water supply. To accomplish this task, this paper explores various methods for demand forecasting, such as Seasonal ARIMA, BATS and Support Vector Machine, and presents a set of statistically validated time series models. These models, integrated with a Model Predictive Control (MPC) strategy addressed in this paper, allow to account for an accurate on-line forecasting and flow management of a DWN.

Abstract-This paper addresses the management of drinking water networks (DWNs) regarding a multi-objective cost function by means of economically-oriented model predictive control (EMPC) strategies. Specifically, assuming the water demand and the energy price as periodically time-varying signals, this paper shows that the EMPC framework is flexible to enhance the control of DWNs without relying on hierarchical control schemes that require the use of real-time optimisers (RTO) or steady-state target optimisers (SSTO) in an upper layer. Four different MPC strategies are discussed in this paper: a hierarchical two-layer approach, a standard EMPC where the multi-objective cost function is optimised directly, and two different modifications of the latter, which are meant to overcome possible feasibility losses in the presence of changing operating patterns. The discussed schemes are tested and compared by means of a case study taken from a part of the Barcelona DWN.

Control of drinking water networks is an arduous task given their size and the presence of uncertainty in water demand. It is necessary to impose different constraints for ensuring a reliable water supply in the most economic and safe ways. To cope with uncertainty in system disturbances due to the stochastic water demand/consumption, and optimize operational costs, this paper proposes three stochastic model predictive control (MPC) approaches, namely: chance-constrained MPC, tree-based MPC, and multiplescenarios MPC. A comparative assessment of these approaches is performed when they are applied to real case studies, specifically, a sector and an aggregate version of the Barcelona drinking water network in Spain.

This paper presents a constrained Model Predictive Control (MPC) strategy enriched with soft-control techniques as neural networks and fuzzy logic, to incorporate self-tuning capabilities and reliability aspects for the management of drinking water networks (DWNs). The control system architecture consists in a multilayer controller with three hierarchical layers: learning and planning layer, supervision and adaptation layer, and feedback control layer. Results of applying the proposed approach to the Barcelona DWN show that the quasi-explicit nature of the proposed adaptive predictive controller leads to improve the computational time, especially when the complexity of the problem structure can vary while tuning the receding horizons.

Abstract-This paper presents a model predictive control strategy to assure reliability in drinking water networks given a customer service level and a forecasting demand. The underlying idea concerns a two-layer hierarchical control structure. The upper layer performs a local steady-state optimization to set up an inventory replenishment policy based on dynamic safety stocks for each tank in the network. At the same stage, actuators health is revised to set up their next maximum allowable degradation in order to efficiently distribute overall control effort and guarantee system availability. In the lower layer, a model predictive control algorithm is implemented to compute optimal control set-points to minimize a multiobjective cost function. Simulation results in the Barcelona drinking water network have shown the effectiveness of the dynamic safety stocks allocation and the actuators health monitoring to assure service reliability and optimizing network operational costs.

In this chapter, a multi-layer decentralized model predictive control (ML-DMPC) approach is proposed and designed for its application to large-scale networked systems (LSNS). This approach is based on the periodic nature of the system disturbance and the availability of both static and dynamic models of the LSNS. Hence, the topology of the controller is structured in two layers. First, an upper layer is in charge of achieving the global objectives from a set O of control objectives given for the LSNS. This layer works with a sampling time ∆t 1 , corresponding to the disturbances period. Second, a lower layer, with a sampling time ∆t 2 , ∆t 1 > ∆t 2 , is in charge of computing the references for the system actuators in order to satisfy the local objectives from the set of control objectives O. A system partitioning allows to establish a hierarchical flow of information between a set C of controllers designed based on model predictive control (MPC). Therefore, the whole proposed ML-DMPC strategy results in a centralized optimization problem for considering the global control objectives, followed of a decentralized scheme for reaching the local control objectives. The proposed approach is applied to a real case study: the water transport network of Barcelona (Spain). Results obtained with selected simulation scenarios show the effectiveness of the proposed ML-DMPC strategy in terms of system modularity, reduced computational burden and, at the same time, the admissible loss of performance with respect to a centralized MPC (CMPC) strategy.