Economic MPC with periodic terminal constraints of nonlinear differential-algebraic-equation systems: Application to drinking water networks

© 2026 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksIn this paper, an Economic Model Predictive Control (EMPC) strategy with periodic terminal constraints is addressed for nonlinear differential-algebraic-equation systems with an application to Drinking Water Networks (DWNs). DWNs have some periodic behaviours because of the daily seasonality of water demands and electrical energy price. The periodic terminal constraint and economic terminal cost are implemented in the EMPC controller design for the purpose of achieving convergence. The feasibility of the proposed EMPC strategy when disturbances are considered is guaranteed by means of soft constraints implemented by using slack variables. Finally, the comparison results in a case study of the D-Town water network is provided by applying the EMPC strategy with or without periodic terminal constraints.Accepted versio

Economic health-aware LPV-MPC based on system reliability assessment for water transport network

This paper proposes a health-aware control approach for drinking water transport networks. This approach is based on an economic model predictive control (MPC) that considers an additional goal with the aim of extending the components and system reliability. The components and system reliability are incorporated into the MPC model using a Linear Parameter Varying (LPV) modeling approach. The MPC controller uses additionally an economic objective function that determines the optimal filling/emptying sequence of the tanks considering that electricity price varies between day and night and that the demand also follows a 24-h repetitive pattern. The proposed LPV-MPC control approach allows considering the model nonlinearities by embedding them in the parameters. The values of these varying parameters are updated at each iteration taking into account the new values of the scheduling variables. In this way, the optimization problem associated with the MPC problem is solved by means of Quadratic Programming (QP) to avoid the use of nonlinear programming. This iterative approach reduces the computational load compared to the solution of a nonlinear optimization problem. A case study based on the Barcelona water transport network is used for assessing the proposed approach performance.Peer ReviewedPostprint (published version

Leak localization in water distribution networks using pressure and data-driven classifier approach

Leaks in water distribution networks (WDNs) are one of the main reasons for water loss during fluid transportation. Considering the worldwide problem of water scarcity, added to the challenges that a growing population brings, minimizing water losses through leak detection and localization, timely and efficiently using advanced techniques is an urgent humanitarian need. There are numerous methods being used to localize water leaks in WDNs through constructing hydraulic models or analyzing flow/pressure deviations between the observed data and the estimated values. However, from the application perspective, it is very practical to implement an approach which does not rely too much on measurements and complex models with reasonable computation demand. Under this context, this paper presents a novel method for leak localization which uses a data-driven approach based on limit pressure measurements in WDNs with two stages included: (1) Two different machine learning classifiers based on linear discriminant analysis (LDA) and neural networks (NNET) are developed to determine the probabilities of each node having a leak inside a WDN; (2) Bayesian temporal reasoning is applied afterwards to rescale the probabilities of each possible leak location at each time step after a leak is detected, with the aim of improving the localization accuracy. As an initial illustration, the hypothetical benchmark Hanoi district metered area (DMA) is used as the case study to test the performance of the proposed approach. Using the fitting accuracy and average topological distance (ATD) as performance indicators, the preliminary results reaches more than 80% accuracy in the best cases.Peer ReviewedPostprint (published version

Non-linear economic model predictive control of water distribution networks

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/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.Peer ReviewedPostprint (author's final draft

Two-layer scheduling scheme for pump stations

In this paper, a two-layer scheduling scheme for pump stations in a water distribution network has been proposed. The upper layer, which works in one-hour sampling time, uses Model Predictive Control (MPC) to produce continuous flow set-points for the lower layer. While in the lower layer, a scheduling algorithm has been used to translate the continuous flow set-points to a discrete (ON-OFF) control operation sequence of the pump stations with the constraints that pump stations should draw the same amount of water as the continuous flow set-points provided by the upper layer. The tuning parameters of such algorithm are the lower layer control sampling period and the number of parallel pumps in the pump station. The proposed method has been tested in the Richmond case study.Peer ReviewedPostprint (published version

Nonlinear Systems Identification Using Additive Dynamic Neural Networks--Two On Line Approaches.

This paper proposes a class of additive dynamic connectionist (ADC) models for identification of unknown dynamic systems. These models work in continuous time and are linear in their parameters. Also, for this kind of model two on-line learning or parameter adaptation algorithms are developed: one based on gradient techniques and sensitivity analysis of the model output trajectories versus the model parameters and the other based on variational calculus, that lead to an off-line solution and an invariant imbedding technique that converts the off-line solution to an on-line one. These learning methods are developed using matrix calculus techniques in order to implement them in an automatic manner with the help of a symbolic manipulation package. The good behavior of the class of identification models and the two learning methods is tested on two simulated plants and a data set from a real plant and compared, in this case, with a feedforward static (FFS) identifier.Peer Reviewe

Multi-layer model predictive control of regional water networks: application to the Catalunya case study

A multi-layer model predictive control (MPC) scheme with temporal multi-level coordination for regional water networks is proposed. First, a multi-layer control structure resulting from a functional decomposition of water network is briefly presented. Inside each layer, a MPC based controller is used. Between related layers, a temporal multi-level coordination mechanism is used to generate control strategies which consider objectives and time scales of both layers. The proposed approach will be applied to the Catalunya Regional Water Network. The paper presents the results based on an aggregate model of this network.Peer ReviewedPostprint (author’s final draft

Fault-tolerant periodic economic model predictive control of differential-algebraic-equation systems

© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksThis paper addresses a fault-tolerant periodic economic model predictive control (MPC) strategy for differential-algebraic-equation (DAE) systems. Fault tolerance evaluation of the proposed economic MPC strategy uses set computations and a performance degradation analysis. By means of the set computations, the feasible solution set (including system states and control inputs) can be determined as well as the admissible performance set can be obtained when system reconfiguration or fault accommodation strategies are used. The proposed control strategy allows to carry out an analysis of performance degradation by using the feasible and admissible performance set. As a result, if the performance degradation is accepted, the economic MPC controller can be applied using system reconfiguration or fault accommodation. Finally, the proposed fault-tolerant MPC strategy is verified through an illustrative example.Accepted versio

Set-membership approach and Kalman observer based on zonotopes for discrete-time descriptor systems

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper proposes a set-membership state estimator and a zonotopic Kalman observer for discrete-time descriptor systems. Both approaches are developed in a set-based context considering system disturbances, measurement noise, and unknown inputs. This set-membership state estimation approach determines the set of consistent states with the model and measurements by constructing a parameterized intersection zonotope. Two methods to minimize the size of this intersection zonotope are provided: one inspired by Kalman filtering and the other based on solving an optimization problem involving a series of linear matrix inequalities. Additionally, we propose a zonotopic Kalman observer for discrete-time descriptor systems. Moreover, the relationship between both approaches is discussed. In particular, it is proved that the zonotopic Kalman observer in the current estimation type is equivalent to the set-membership approach. Finally, a numerical example is used to illustrate and compare the effectiveness of the proposed approaches.Peer ReviewedPostprint (author's final draft

Health-aware LPV-MPC based on a reliability-based remaining useful life assessment

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/One of the relevant information provided by the prognostics and health management algorithms is the estimation of the Remaining Useful Life (RUL). The prediction of the expected RUL is very useful to decrease maintenance cost, operational downtime and safety hazards. This paper proposes a new strategy of health-aware Model Predictive Control (MPC) for a Linear Parameter Varying (LPV) system that includes as an additional goal extending the system RUL via their estimation using reliability tools. In this approach, the RUL maximization is included in the objective function of the LPV-MPC controller. The RUL is included in the MPC model as an extra parameter varying equation that considers the control action as scheduling variable. The proposed control approach allows the controller to accommodate to the parameter changes. Through computing an estimation of the state variables during prediction, the MPC model can be modified to the estimated state evolution at each time instant. Moreover, for solving the optimization problem by using a series of Quadratic Programs (QP) in each time instant, a new iterative approach is exhibited, which improves the computational efficiency. A pasteurization plant control system is used as a case study to illustrate the performance of the proposed approach.Peer ReviewedPostprint (author's final draft