Evolutionary-game-based dynamical tuning for multi-objective model predictive control

Model predictive control (MPC) is one of the most used optimization-based control strategies for large-scale systems, since this strategy allows to consider a large number of states and multi-objective cost functions in a straightforward way. One of the main issues in the design of multi-objective MPC controllers, which is the tuning of the weights associated to each objective in the cost function, is treated in this work. All the possible combinations of weights within the cost function affect the optimal result in a given Pareto front. Furthermore, when the system has time-varying parameters, e.g., periodic disturbances, the appropriate weight tuning might also vary over time. Moreover, taking into account the computational burden and the selected sampling time in the MPC controller design, the computation time to find a suitable tuning is limited. In this regard, the development of strategies to perform a dynamical tuning in function of the system conditions potentially improves the closed-loop performance. In order to adapt in a dynamical way the weights in the MPC multi-objective cost function, an evolutionary-game approach is proposed. This approach allows to vary the prioritization weights in the proper direction taking as a reference a desired region within the Pareto front. The proper direction for the prioritization is computed by only using the current system values, i.e., the current optimal control action and the measurement of the current states, which establish the system cost function over a certain point in the Pareto front. Finally, some simulations of a multi-objective MPC for a real multi-variable case study show a comparison between the system performance obtained with static and dynamical tuning.Peer ReviewedPostprint (author's final draft

Dynamical tuning for MPC using population games: a water supply network application

ISA Transactions Best Paper Award 2018Model predictive control (MPC) is a suitable strategy for the control of large-scale systems that have multiple design requirements, e.g., multiple physical and operational constraints. Besides, an MPC controller is able to deal with multiple control objectives considering them within the cost function, which implies to determine a proper prioritization for each of the objectives. Furthermore, when the system has time-varying parameters and/or disturbances, the appropriate prioritization might vary along the time as well. This situation leads to the need of a dynamical tuning methodology. This paper addresses the dynamical tuning issue by using evolutionary game theory. The advantages of the proposed method are highlighted and tested over a large-scale water supply network with periodic time-varying disturbances. Finally, results are analyzed with respect to a multi-objective MPC controller that uses static tuning.Peer ReviewedAward-winningPostprint (author's final draft

Dynamical tuning for MPC using population games: a water supply network application

ISA Transactions Best Paper Award 2018Model predictive control (MPC) is a suitable strategy for the control of large-scale systems that have multiple design requirements, e.g., multiple physical and operational constraints. Besides, an MPC controller is able to deal with multiple control objectives considering them within the cost function, which implies to determine a proper prioritization for each of the objectives. Furthermore, when the system has time-varying parameters and/or disturbances, the appropriate prioritization might vary along the time as well. This situation leads to the need of a dynamical tuning methodology. This paper addresses the dynamical tuning issue by using evolutionary game theory. The advantages of the proposed method are highlighted and tested over a large-scale water supply network with periodic time-varying disturbances. Finally, results are analyzed with respect to a multi-objective MPC controller that uses static tuning.Peer ReviewedAward-winningPostprint (author's final draft

Chance-constrained model predictive control for drinking water networks

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 of applying the proposed approach to a real case study - the Barcelona DWN (Spain) - have shown that the network performance (in terms of operational costs) and the necessary back-off (to cope with stochastic disturbances) are optimised simultaneously within a single problem, keeping tractability of the solution, even in large-scale networks. The general formulation of the approach and the automatic computation of proper back-off within the MPC framework replace the need of experience-based heuristics or bi-level optimisation schemes that might compromise the trade-off between profits, reliability and computational burden.This work has been partially supported by the EU Project EFFINET (FP7-ICT-2011-8-31855) and the DGR of Generalitat de Catalunya (SAC group Ref. 2009/SGR/1491).Peer Reviewe

On the comparison of predictive control and command governor approaches for operational management of drinking water networks: a case study

This paper evaluates the application of command governor (CG) strategy for the operational control of drinking water networks (DWN) given their large-scale and complex nature, the permanent and relevant effect of the disturbances (water demands) and their marginal stability feature. Moreover, the performance improvement offered by CG is compared with the application of model predictive control for the same management purposes and in the same context. The paper also discusses the effectiveness of both strategies and highlights the advantages of each approach. The Barcelona DWN is considered as case study for the undertaken assessment analysis.Peer ReviewedPostprint (author’s final draft

Two-layer scheduling scheme for pump stations

Trabajo presentado a la IEEE Conference on Control Applications (CCA) celebrada en Juan-les-Pins, Antibes (Francia) del 8 al 10 de octubre de 2014.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.This work has been funded by the Spanish Ministry of Science and Technology through the project CYCYT WATMAN DPI2009-13744 and also funded by EFFINET grant FP7-ICT-2012-318556 of the European Commission.Peer Reviewe

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

Water demand forecasting for the optimal operation of large-scale drinking water networks: the Barcelona case study

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

On model predictive control for economic and robust operation of generalised flow-based networks

This thesis is devoted to design Model Predictive Control (MPC) strategies aiming to enhance the management of constrained generalised flow-based networks, with special attention to the economic optimisation and robust performance of such systems. Several control schemes are developed in this thesis to exploit the available economic information of the system operation and the disturbance information obtained from measurements and forecasting models. Dynamic network flows theory is used to develop control-oriented models that serve to design MPC controllers specialised for flow networks with additive disturbances and periodically time-varying dynamics and costs. The control strategies developed in this thesis can be classified in two categories: centralised MPC strategies and non-centralised MPC strategies. Such strategies are assessed through simulations of a real case study: the Barcelona drinking water network (DWN). Regarding the centralised strategies, different economic MPC formulations are first studied to guarantee recursive feasibility and stability under nominal periodic flow demands and possibly time-varying economic parameters and multi-objective cost functions. Additionally, reliability-based MPC, chance-constrained MPC and tree-based MPC strategies are proposed to address the reliability of both the flow storage and the flow transportation tasks in the network. Such strategies allow to satisfy a customer service level under future flow demand uncertainty and to efficiently distribute overall control effort under the presence of actuators degradation. Moreover, soft-control techniques such as artificial neural networks and fuzzy logic are used to incorporate self-tuning capabilities to an economic certainty-equivalent MPC controller. Since there are objections to the use of centralised controllers in large-scale networks, two non-centralised strategies are also proposed. First, a multi-layer distributed economic MPC strategy of low computational complexity is designed with a control topology structured in two layers. In a lower layer, a set of local MPC agents are in charge of controlling partitions of the overall network by exchanging limited information on shared resources and solving their local problems in a hierarchical-like fashion. Moreover, to counteract the loss of global economic information due to the decomposition of the overall control task, a coordination layer is designed to influence non-iteratively the decision of local controllers towards the improvement of the overall economic performance. Finally, a cooperative distributed economic MPC formulation based on a periodic terminal cost/region is proposed. Such strategy guarantees convergence to a Nash equilibrium without the need of a coordinator and relies on an iterative and global communication of local controllers, which optimise in parallel their control actions but using a centralised model of the network.Esta tesis se enfoca en el diseño de estrategias de control predictivo basado en modelos (MPC, por sus siglas en inglés) con la meta de mejorar la gestión de sistemas que pueden ser descritos por redes generalizadas de flujo y que están sujetos a restricciones, enfatizando especialmente en la optimización económica y el desempeño robusto de tales sistemas. De esta manera, varios esquemas de control se desarrollan en esta tesis para explotar tanto la información económica disponible de la operación del sistema como la información de perturbaciones obtenida de datos medibles y de modelos de predicción. La teoría de redes dinámicas de flujo es utilizada en esta tesis para desarrollar modelos orientados a control que sirven para diseñar controladores MPC especializados para la gestión de redes de flujo que presentan tanto perturbaciones aditivas como dinámicas y costos periódicamente variables en el tiempo. Las estrategias de control propuestas en esta tesis se pueden clasificar en dos categorías: estrategias de control MPC centralizado y estrategias de control MPC no-centralizado. Dichas estrategias son evaluadas mediante simulaciones de un caso de estudio real: la red de transporte de agua potable de Barcelona en España. En cuanto a las estrategias de control MPC centralizado, diferentes formulaciones de controladores MPC económicos son primero estudiadas para garantizar factibilidad recursiva y estabilidad del sistema cuya operación responde a demandas nominales de flujo periódico, a parámetros económicos posiblemente variantes en el tiempo y a funciones de costo multi-objetivo. Adicionalmente, estrategias de control MPC basado en fiabilidad, MPC con restricciones probabilísticas y MPC basado en árboles de escenarios son propuestas para garantizar la fiabilidad tanto de tareas de almacenamiento como de transporte de flujo en la red. Tales estrategias permiten satisfacer un nivel de servicio al cliente bajo incertidumbre en la demanda futura, así como distribuir eficientemente el esfuerzo global de control bajo la presencia de degradación en los actuadores del sistema. Por otra parte, técnicas de computación suave como redes neuronales artificiales y lógica difusa se utilizan para incorporar capacidades de auto-sintonía en un controlador MPC económico de certeza-equivalente. Dado que hay objeciones al uso de control centralizado en redes de gran escala, dos estrategias de control no-centralizado son propuestas en esta tesis. Primero, un controlador MPC económico distribuido de baja complejidad computacional es diseñado con una topología estructurada en dos capas. En una capa inferior, un conjunto de controladores MPC locales se encargan de controlar particiones de la red mediante el intercambio de información limitada de los recursos físicos compartidos y resolviendo sus problemas locales de optimización de forma similar a una secuencia jerárquica de solución. Para contrarrestar la pérdida de información económica global que ocurra tras la descomposición de la tarea de control global, una capa de coordinación es diseñada para influenciar no-iterativamente la decisión de los controles locales con el fin de lograr una mejora global del desempeño económico. La segunda estrategia no-centralizada propuesta en esta tesis es una formulación de control MPC económico distribuido cooperativo basado en una restricción terminal periódica. Tal estrategia garantiza convergencia a un equilibrio de Nash sin la necesidad de una capa de coordinación pero requiere una comunicación iterativa de información global entre todos los controladores locales, los cuales optimizan en paralelo sus acciones de control utilizando un modelo centralizado de la red

Centralized and distributed command governor approaches for water supply systems management

© 2018 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 works.This paper evaluates the applicability of Command Governor (CG) strategies to the optimal management of Drinking Water Supply Systems (DWSS) in both centralized and distributed ways. It will be shown that CG approaches provide an adequate framework for addressing the management of these large-scale interconnected systems in the presence of periodically time-varying disturbances (water demands) that can be anticipated by using time-series forecasting approaches. The proposed centralized and distributed CG schemes are presented, discussed and compared when applied to the management of DWSS considering the same set of operational goals in all cases. The paper illustrates the effectiveness of all strategies using the Barcelona DWSS as a case study and highlighting the advantages of each approach.Peer ReviewedPostprint (author's final draft