Distributed population dynamics: Optimization and control applications

Population dynamics have been widely used in the design of learning and control systems for networked engineering applications, where the information dependency among elements of the network has become a relevant issue. Classic population dynamics (e.g., replicator, logit choice, Smith, and projection) require full information to evolve to the solution (Nash equilibrium). The main reason is that classic population dynamics are deduced by assuming well-mixed populations, which limits the applications where this theory can be implemented. In this paper, we extend the concept of population dynamics for nonwell-mixed populations in order to deal with distributed information structures that are characterized by noncomplete graphs. Although the distributed population dynamics proposed in this paper use partial information, they preserve similar characteristics and properties of their classic counterpart. Specifically, we prove mass conservation and convergence to Nash equilibrium. To illustrate the performance of the proposed dynamics, we show some applications in the solution of optimization problems, classic games, and the design of distributed controllers.This work has been supported by COLCIENCIAS–COLFUTURO, grants No: 528 and 6172; and by Project ALTERNAR, Acuerdo 005, 07/19/13 CTeI–SGR–Narino, Colombia.Peer reviewe

Constrained distributed optimization based on population dynamics

Trabajo presentado a la 53rd IEEE Conference on Decision and Control (CDC 2014), celebrada del 15 al 17 de diciembre en Los Angeles, California (US).This paper proposes a novel methodology for solving constrained optimization problems in a distributed way, inspired by population dynamics and adding dynamics to the population masses. The proposed methodology divides the problem into smaller problems, whose feasible regions vary over time achieving an agreement to solve the global problem. The methodology also guarantees attraction to the feasible region and allows to have few changes in the decision-making design, when the network suffers the addition or removal of nodes. Simulation results are presented in order to illustrate several cases.J. Barreiro-Gomez is supported by COLCIENCIAS and by the Agència de Gestió d’Ajust Universitaris i de Recerca AGAUR. This work has been supported by the projects COLCIENCIAS 548/2012, and the EU project EFFINET (Ref. FP7-ICT-2011-8-31855)Peer Reviewe

Distributed control of drinking water networks using population dynamics: Barcelona case study

Trabajo presentado a la 53rd IEEE Conference on Decision and Control (CDC 2014), celebrada del 15 al 17 de diciembre en Los Angeles, California (US).Large-scale network systems involve a large number of variables, making the design of real-time controllers challenging. A distributed controller design allows to reduce computational requirements since tasks may be divided into different subsystems, making possible to guarantee real-time processing. This paper proposes a constrained optimization based distributed control design by applying a novel population and masses dynamics approach. The distributed controller design is applied to the Barcelona Drinking Water Network (DWN) in order to illustrate its effectiveness in the control performance.This work has been partially supported by the projects COLCIENCIAS 548/2012, ECOCIS (Ref. DPI2013-48243-C2-1-R) and EFFINET (Ref. FP7-ICT-2011-8-31855). J. Barreiro-Gómez is supported by COLCIENCIAS and by the Agència de Gestió d’Ajust Universitaris i de Recerca AGAUR.Peer Reviewe

Decentralized control for urban drainage systems via population dynamics: Bogotá case study

Trabajo presentado a la European Control Conference celebrada en Linz (Alemania) del 15 al 17 de julio de 2015.Control of Urban Drainage Systems (UDS) is studied for cases in which the distribution of run–off through the channels of a system is inefficient, i.e. when the capacity of some structures is not used optimally. In this paper, a decentralized population-dynamics-based control for UDS is presented, particularly using the replicator and projection dynamics. For the design, a methodology to make a partitioning of the system is introduced, and the design of a population–dynamics–based control per each partition is proposed. Moreover, a stability analysis of the closed–loop system is made by using passivity theory. Finally, simulation results show the proposed approach performance in a segment of the Bogota stormwater UDS case study.COLCIENCIAS supports J. Barreiro-Gómez and G. Obando. Agència de Gestió d’Ajust Universitaris i de Recerca AGAUR supports J. Barreiro-Gómez. This work has been partially supported by the projects “Drenaje urbano y cambio climático: Hacia los sistemas de alcantarillados del futuro. Fase II. COLCIENCIAS 633/2013”, ECOCIS (Ref. DPI2013-48243-C2-1-R), and EFFINET (Ref. FP7-ICT-2011-8-31855).Peer Reviewe

On the modeling and real-time control of urban drainage systems: A survey

Trabajo presentado a la 11th International Conference on Hydroinformatics celebrada en New York (US) del 17 al 21 de agosto de 2014.Drainage networks are complex systems composed by several processes including recollection, transport, storing, treatment, and releasing the water to a receiving environment. The way Urban Drainage Systems (UDS) manage wastewater is through the convenient handling of active elements such as gates (redirection and/or retention), storing tanks, and pumping stations, when needed. Therefore, modeling and control of UDS basically consists in knowing and representing the (dynamical) behavior of these elements and managing them properly in order to achieve a given set of control objectives, such as minimization of flooding in streets or maximization of treated wastewater in the system. Given the large number of elements composing an UDS and the interaction between them, management and control strategies may depend on highly complex system models, which implies the explicit difficulty for designing real-time control (RTC) strategies. This paper makes a review of the models used to describe, simulate, and control UDS, proposes a revision of the techniques and strategies commonly used for the control UDS, and finally compares several control strategies based on a case study.This work has been partially supported by project N°548-2012 “Drenaje Urbano y Cambio Climático: Hacia los Sistemas de Alcantarillado del Futuro.”, Mexichem Colombia S.A, the scholarships of Colciencias N°567-2012 and 647-2013, and the EU Project EFFINET (FP7-ICT-2011-8-31855) and the DGR of Generalitat de Catalunya (SAC group Ref. 2009/SGR/1491).Peer Reviewe

Modeling and real-time control of urban drainage systems: A review

Urban drainage systems (UDS) may be considered large-scale systems given their large number of associated states and decision actions, making challenging their real-time control (RTC) design. Moreover, the complexity of the dynamics of the UDS makes necessary the development of strategies for the control design. This paper reviews and discusses several techniques and strategies commonly used for the control of UDS. Moreover, the models to describe, simulate, and control the transport of wastewater in UDS are also reviewed.This work has been partially supported by Mexichem, Colombia through the project “Drenaje Urbano y Cambio Climático: Hacia los Sistemas de Alcantarillado del Futuro.” Fase II, with reference No. 548-2012, the scholarships of Colciencias No. 567-2012 and 647-2013, and the project ECOCIS (Ref. DPI2013-48243-C2-1-R).Peer Reviewe

On The Modeling And Real-Time Control Of Urban Drainage Systems: A Survey

Drainage network are complex systems composed by several processes including recollection, transport, storing, wastewater and/or rain treatment, and return of the water to a receiving environment. Urban drainage systems (UDS) involve most of these processes inside cities and can be either separate or combined systems, depending on how wastewater and rainwater are managed. The way UDS manage the wastewater is through the convenient handling of active elements such as gates (redirection and/or retention), storing tanks and pumping stations, when needed. Therefore, the modeling and control of UDS basically consists in knowing and representing the (dynamical) behavior of those elements and manage them properly in order to achieve a given set of control objectives, such as minimization of flooding in streets or maximization of treated wastewater in the system. Given the large number of elements composing a UDS and the interaction between them, management and control strategies may depend on highly complex system models, what implies the explicit difficulty for designing real-time control strategies. This paper makes a review on the huge world of models used to describe, simulate, and control UDS. Moreover, a revision of the techniques and strategies commonly used for the control of these systems is also presented and discussed. Mechanisms that ensure the correct operation of the UDS under presence of failures or communication flaws in the system are considered as well

Careón ophiolite, NW Spain: Suprasubduction zone setting for the youngest Rheic Ocean fl oor

The Careón ophiolite (Galicia, NW Iberian Massif) shows lithological and geochemical features suggestive of an origin in a suprasubduction zone setting. As with other Devonian ophiolites in the European Variscan belt, it was generated within a contracting Rheic Ocean. This setting and the general absence of large Silurian-Devonian volcanic arcs on both of the Rheic Ocean margins strongly suggest that this ocean was closed by intraoceanic subduction directed to the north. This subduction removed the older normal (N) mid-oceanic-ridge basalt (MORB) oceanic lithosphere and gave rise to a limited volume of new suprasubduction zone oceanic lithosphere. The Careón ophiolite is a key element in understanding the evolution of the Rheic Ocean, which was the main oceanic domain that closed during the Paleozoic convergence of Gondwana and Laurussia, preceding the assembly of Pange

The Role of Population Games in the Design of Optimization-Based Controllers

This book reports on the implementation of evolutionary-game theory in the design of distributed optimization-based controllers. First, it discusses how the classical population-game approach can contribute to and complement the design of optimization-based controllers. It shows how the features of this approach can be exploited to extend their capabilities in the solution of distributed optimization problems, and examines density games in order to consider multiple coupled constraints and preserve the non-centralized information requirements. Furthermore, it establishes a close relationship between the possible interactions among agents in a population with constrained information sharing among different local controllers. It also discusses coalitional games, focusing on the Shapley power index and proposes an alternative method of computing the latter, which reduces computational time, as well as a different way of finding it using distributed communication structures. All the proposed strategies are then tested on various control problems, such as those related to the Barcelona water supply network, multiple continuous stirred tank reactors, various unmanned aerial vehicle systems, and a water distribution system. This thesis, examined at the Universitat Politècnica de Catalunya and Universidad de los Andes in 2017, received the award for best thesis in control from the control group of the Spanish Committee of Automatic Control (CEA) in the same year

The role of population games in the design of optimization-based controllers: a large-scale insight

Universitat Politècnica de Catalunya (UPC). Departament d’Enginyeria de Sistemes, Automàtica i Informàtica Industrial. Doctoral Program: Automatic Control, Robotics and Computer Vision. Universidad de los Andes (UniAndes). Departamento de Ingeniería Eléctrica y Electrónica. Doctoral Program: Engineering. This PhD thesis was completed at: Institut de Robòtica i Informàtica Industrial, CSIC-UPC, and Universidad de los Andes.[EN]: This thesis is mainly devoted to the study of the role of evolutionary-game theory in the design of distributed optimization-based controllers. Game theoretical approaches have been used in several engineering fields, e.g., drainage wastewater systems, bandwidth allocation, wireless networks, cyber security, congestion games, wind turbines, temperature control, among others. On the other hand, a specific class of games, known as population games, have been mainly used in the design of controllers to manage a limited resource. This game approach is suitable for resource allocation problems since, under the framework of full-potential games, the population games can satisfy a unique coupled constraint while maximizing a potential function. First, this thesis discusses how the classical approach of the population games can contribute and complement the design of optimization-based controllers. Therefore, this dissertation assigns special interest on how the features of the population-game approach can be exploited extending their capabilities in the solution of distributed optimization problems. In addition, density games are studied in order to consider multiple coupled constraints and preserving the non-centralized information requirements. Furthermore, it is established a close relationship between the possible interactions among agents in a population with the constrained information sharing among different local controllers. On the other hand, coalitional games are discussed focusing on the Shapley power index. This power index has been used to assign an appropriate rewarding to players in function of their contributions to all possible coalitions. Even though this power index is quite useful in the engineering context, since it involves notions of fairness and/or relevance (how important players are), the main difficulty of the implementation of the Shapley value in engineering applications is related to the high computational burden. Therefore, this dissertation studies the Shapley value in order to propose an alternative manner to compute it reducing computational time, and a different way to find it by using distributed communication structures is presented. The studied game theoretical approaches are suitable for the modeling of rational agents involved in a strategic constrained interaction, following local rules and making local decisions in order to achieve a global objective. Making an analogy, distributed optimization-based controllers are composed of local controllers that compute optimal inputs based on local information (constrained interactions with other local controllers) in order to achieve a global control objective. In addition to this analogy, the features that relate the Nash equilibrium with the Karush-Kuhn-Tucker conditions for a constrained optimization problem are exploited for the design of optimization-based controllers, more specifically, for the design of model predictive controller. Moreover, the design of non-centralized controllers is directly related to the partitioning of a system, i.e., it is necessary to represent the whole system as the composition of multiple sub-systems. This task is not atrivial procedure since several considerations should be taken into account, e.g., availability of information, dynamical coupling in the system, regularity in the amount of variables for each sub-system, among others. Then, this doctoral dissertation also discusses the partitioning problem for large-scale systems and the role that this procedure plays in the design of distributed optimization-based controllers. Finally, dynamical partitioning strategies are presented with distributed population-games-based controllers. Some engineering applications are presented to illustrate and test the performance of all the proposed control strategies, e.g., the Barcelona water supply network, multiple continuous stirred tank reactors, system of multiple unmanned aerial vehicles.[ES]: Esta tesis doctoral consiste principalmente en el estudio del rol que desempeña la teoría de juegos evolutiva en el diseño de controladores distribuidos basados en optimización. Diversos enfoques de la teoría de juegos han sido usados en múltiples campos de la ingeniera, por ejemplo, en sistemas de drenaje urbano, para la asignación de anchos de banda, en redes inalámbricas, en ciber-seguridad, en juegos de congestión, turbinas eólicas, control de temperatura, entre otros. Por otra parte, una clase especifica de juegos, conocidos como juegos poblacionales, se han usado principalmente en el diseño de controladores encargados de determinar la apropiada asignación de recursos. Esta clase de juegos es apropiada para problemas de distribución dinámica de recursos dado que, en el contexto de juegos poblacionales, los juegos poblacionales pueden ser usados para maximizar una función potencial mientras se satisface una restricción acoplada. Primero, esta tesis doctoral presenta como el enfoque clásico de los juegos poblacionales pueden contribuir y complementar en el diseño de controladores basados en optimización. Posteriormente, esta disertación concentra su atención en cómo las características de los juegos poblacionales pueden ser aprovechadas y extendidas para dar solución a problemas de optimización de forma distribuida. Adicionalmente, los juegos con dependencia de densidad son estudiados con el fin de considerar múltiples restricciones mientras se preservan las características no centralizadas de los requerimientos de información. Finalmente, se establece una estrecha relación entre las posibles interacciones de los agentes en una población y las restricciones de intercambio de información entre diversos controladores locales. También, se desarrolla una discusión sobre los juegos cooperativos y el índice de poder conocido como el valor de Shapley. Este índice de poder ha sido usado para la apropiada asignación de beneficios para un jugador en función de sus contribuciones a todas las posibles coaliciones que pueden formarse. Aunque este índice de poder es de gran utilidad en el contexto ingenieril, ya que involucra nociones de justicia y/o relevancia, la principal dificultad para implementar el valor de Shapley en aplicaciones de ingeniería está asociado a los altos costos computacionales para encontrarlo. En consecuencia, esta disertación doctoral estudia el valor de Shapley con el fin de ofrecer una alternativa para calcular este índice de poder reduciendo los costos computacionales e incluso contemplando estructuras distribuidas de comunicación. Los enfoques de la teoría de juegos estudiados son apropiados para el modelamiento de agentes racionales involucrados en una interacción estratégica con restricciones, siguiendo reglas locales y tomando decisiones locales para alcanzar un objetivo global. Realizando unaanalogía, los controladores distribuidos basados en optimización están compuestos por controladores locales que calculan acciones óptimas basados en información local (considerando interacciones restringidas con otros controladores locales) con el fin de alcanzar un objetivo global. Adicional a esta analogía, las características que relacionan el equilibrio de Nash con las condiciones de Karush-Kuhn-Tucker en un problema de optimizaciones con restricciones son aprovechadas para el diseño de controladores basados en optimización, más específicamente, para el diseño de controladores predictivos. Por otra parte, el diseño de controladores no centralizados está directamente relacionado con el particionado de un sistema, es decir, es necesario representar el sistema en su totalidad por medio del conjunto de varios sub-sistemas. Esta tarea no es un procedimiento trivial puesto que es necesario tener en cuenta varias consideraciones, por ejemplo, la disponibilidad de información, el acople dinámico en el sistema, la regularidad en cuanto a la cantidad de variables en cada sub-sistema, entre otras. Por lo tanto, esta disertación doctoral también desarrolla una discusión alrededor del problema de particionado para sistemas de gran escala y respecto al rol que este procedimiento de particionado juega en el diseño de controladores distribuidos basados en optimización. Finalmente, se presentan estrategias de particionado dinámico junto con controladores basados en juegos poblacionales. Algunas aplicaciones en ingeniería son usadas para ilustrar y probar los controladores diseñados por medio de las contribuciones novedosas basadas en teoría de juegos, estas son, la red de agua potable de Barcelona, múltiples reactores, sistema compuesto por varios vehículos aéreos no tripulados y un sistema de distribución de agua.[CA]: Aquesta tesi doctoral consisteix principalment en l'estudi del paper que exerceix la teoria de jocs evolutiva en el disseny de controladors distribuïts basats en optimització. Diversos enfocaments de la teoria de jocs han estat usats en múltiples camps de l'enginyeria, per exemple, en sistemes de drenatge urbà, per a l’assignació d'amples de banda, en xarxes sense fils, a ciber-seguretat, en jocs de congestió, turbines eòliques, control de temperatura, entre altres. D'altra banda, una classe especifica de jocs, coneguts com jocs poblacionals, s'han fet servir principalment en el disseny de controladors encarregats de determinar l'apropiada assignació de recursos. Aquesta classe de jocs és apropiada per a problemes de distribució dinàmica de recursos atès que, en el context de jocs poblacionals, aquests poden ser usats per a maximitzar una funció potencial mentre es satisfà una restricció acoblada. Primer, aquesta tesi doctoral presenta com l'enfocament clàssic dels jocs poblacionals poden contribuir i complementar en el disseny de controladors basats en optimització. Posteriorment, aquesta dissertació concentra la seva atenció en com les característiques dels jocs poblacionals poden ser aprofitades i esteses per donar solució a problemes d’optimització de forma distribuïda. Addicionalment, els jocs amb dependència de densitat són estudiats amb la _finalitat de considerar múltiples restriccions mentre es preserven les característiques no centralitzades dels requeriments d’informació. Finalment, s'estableix una estreta relació entre les possibles interaccions dels agents en una població i les restriccions d'intercanvi d’informació entre diversos controladors locals. També, es desenvolupa una discussió sobre els jocs cooperatius i l’índex de poder conegut com el valor de Shapley. Aquest índex de poder ha estat usat per l'apropiada assignació de beneficis per a un jugador en funció de les seves contribucions a totes les possibles coalicions que poden formar-se. Encara que aquest índex de poder es de gran utilitat en el context de l'enginyeria, ja que involucra nocions de justícia i/o rellevància, la principal dificultat per implementar el valor de Shapley en aplicacions d'enginyeria està associat als alts costos computacionals per trobar-lo. En conseqüència, aquesta dissertació doctoral estudia el valor de Shapley per tal d'oferir una alternativa per calcular aquest índex de poder reduint els costos computacionals i fins i tot contemplant estructures distribuïdes de comunicació. Els enfocaments de la teoria de jocs estudiats són apropiats per al modelatge d'agents racionals involucrats en una interacció estratègica amb restriccions, seguint regles locals i prenent decisions locals per assolir un objectiu global.Realitzant una analogia, els controladors distribuïts basats en optimització estan compostos per controladors locals que calculen accions optimes basats en informació local (considerant interaccions restringides amb altres controladors locals) per tal d'assolir un objectiu global. Addicional a aquesta analogia, les característiques que relacionen l'equilibri de Nash amb les condicions de Karush-Kuhn-Tucker en un problema d’optimització amb restriccions són aprofitades per al disseny de controladors basats en optimització, més específicament, per al disseny de controladors predictius. D'altra banda, el disseny de controladors no centralitzats està directament relacionat amb la partició d'un sistema, és a dir, cal representar el sistema en la seva totalitat per mitjà del conjunt de diversos sub-sistemes. Aquesta tasca no és un procés trivial, ja que cal tenir en compte diverses consideracions, per exemple, la disponibilitat d’informació, l'acoblament dinàmic en el sistema, i la regularitat pel que fa a la quantitat de variables en cada sub-sistema, entre d'altres. Per tant, aquesta dissertació doctoral també desenvolupa una discussió al voltant del problema de partició per a sistemes de gran escala i respecte al paper que aquest procediment de partició juga en el disseny de controladors distribuïts basats en optimització. Finalment, es presenten estratègies de partició dinàmic juntament amb controladors basats en jocs poblacionals. Algunes aplicacions en enginyeria són usades per il·lustrar i provar els controladors dissenyats per mitjà de les contribucions noves basades en teoria de jocs, aquestes són: la xarxa d'aigua potable de Barcelona, múltiples reactors, sistema compost per diversos vehicles aeris no tripulats i un sistema de distribució d'aigua.I sincerely thank Agència de Gestió d’Ajust Universitaris i de Recerca AGAUR for having granted the FI scholarship for me to study the doctoral degree at UPC, and Colciencias for having granted the scholarship/condonable loan (Ref. 6172) for me to study the doctoral degree at UniAndes. I would also like to thank the projects ECOCIS: EConomic Operation of Critical Infrastructure Systems (Ref. DPI2013-48243- C2-1-R), EFFINET: EFFicient Integrated real-time monitoring and control of drinking water NETworks (Ref. FP7-ICT-2011-8-318556), ModCon: Modelado y control de redes de alcantarillado: aplicación en Bogotá (Colombia), and “Drenaje urbano y cambio climático: hacia los sistemas de alcantarillado del futuro. Fase II”, Mexichem, Colombia for partially supporting me.Peer Reviewe