Nash equilibrium seeking in population games under partial information and its application to congestion games

En este artículo, consideramos el marco de dinámicas evolutivas y juegos poblacionales. Para una clase de dinámicas evolutivas y una familia de juegos poblacionales contractivos, desarrollamos un método novedoso para la búsqueda distribuida de equilibrios de Nash bajo información parcial respecto a las decisiones de los demás agentes. La principal contribución es que establecemos condiciones suficientes para garantizar la estabilidad asintótica del conjunto de equilibrios de Nash del juego poblacional subyacente. Además, ilustramos nuestros resultados teóricos en una aplicación numérica de un juego de congestión de gran escala.Juan Martinez-Piazuelo agradece a la Universitat Politécnica de Catalunya y al Banco Santander, España, por la financiación de su beca FPI-UPC. Adicionalmente, los autores agradecen a los proyectos PID2020-115905RB-C21 (L-BEST) y TED2021-129927B-I00 (MASHED), financiados por MCIN/ AEI/10.13039/501100011033 y por la European Union Next GenerationEU/PRTR, por financiar esta investigación. Finalmente, Nicanor Quijano agradece el proyecto BPIN2021000100499, de la asignación para CTeI-SGR y Minciencias.Peer ReviewedPostprint (published version

Microalgae production and maintenance optimization via mixed-integer model predictive control

This paper studies the joint production and maintenance scheduling in microalgae manufacturing systems comprised of multiple machines, which are subject to coupled production demand agreements and operational maintenance constraints. Namely, there are some microalgae production demands to be met over a given horizon, and the maintenance of each microalgae manufacturing unit must be done before a given deadline. Moreover, the number of units whose maintenance can be done simultaneously over the same day is limited, and the units that undergo maintenance cannot contribute to microalgae production during their maintenance day. To solve the considered problem, we design a mixed-integer nonlinear model predictive controller, which is implemented in two optimization stages. The former regards a mixed-integer model predictive control problem, while the latter considers a nonlinear model predictive control problem. The proposed approach allows us to decouple the mixed-integer and nonlinear parts of the whole problem, and thus provides more flexibility on the optimization solvers that can be employed. In addition, the first stage also evaluates the attainability of the demand agreements, and provides a mechanism to minimally adjust such constraints so that their satisfaction can be guaranteed at the second stage. The overall model predictive control approach is based on experimental data collected at VAXA Technologies Ltd., and the effectiveness of the proposed method is validated through numerical simulations including multiple manufacturing units and uncertainties.Juan Martinez-Piazuelo gratefully acknowledges the Universitat Politècnica de Catalunya and Banco Santander for the financial support of his predoctoral grant FPI-UPC. In addition, the authors would like to thank VAXA Technologies Ltd. as well as the project PID2020-115905RB-C21 (L-BEST) funded by MCIN/ AEI /10.13039/501100011033 for supporting this research.Peer ReviewedPostprint (published version

Population-dynamics-assisted coalitional model predictive control for parabolic-trough solar plants

This paper proposes a coalitional model predictive control method for temperature regulation in parabolic-trough solar fields. The global optimization problem is divided into a set of local subproblems that will be solved in parallel by a set of coalitions. However, these local (smaller) problems remain coupled by a common global resource constraint. In this regard, we present a population-dynamics-assisted resource allocation approach to fully decouple the local optimization problems. By doing this, each coalition can address its corresponding optimization problem without relying on the solutions of the other coalitions. To illustrate the proposed methodology, we provide simulation results for a 100-loop parabolic-trough solar collector field.The authors gratefully acknowledge the financial support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (OCONTSOLAR, grant agreement No 789051). In addition, the authors would like to thank the projects PID2020-119476RB-I00 (C3PO-R2D2) and TED2021-129927B-I00 (MASHED) funded by MCIN/ AEI /10.13039/501100011033 and by the “European Union NextGenerationEU/ PRTR” for supporting this research. Finally, Juan Martinez- Piazuelo gratefully acknowledges the Universitat Politècnica de Catalunya and Banco Santander for the financial support of his predoctoral grant FPI-UPC.Peer ReviewedPostprint (published version

Coalitional model predictive control of parabolic-trough solar collector fields with population-dynamics assistance

Parabolic-trough solar collector fields are large-scale systems, so the application of centralized optimizationbased control methods to these systems is often not suitable for real-time control. As such, this paper formulates a novel coalitional control approach as an appropriate alternative to the centralized scheme. The key idea is to split the overall solar collector field into smaller subsystems, each of them governed by a local controller. Then, controllers are clustered into coalitions to solve a local optimization-based problem related to the corresponding subset of subsystems, so that an approximate solution of the original centralized problem can be obtained in a decentralized fashion. However, the operational constraints of the solar collector field couple the optimization problems of the multiple coalitions, thus limiting the ability to solve them in a fully decentralized manner. To overcome this issue, a novel population-dynamics-assisted resource allocation strategy is proposed as a mechanism to decouple the local optimization problems of the multiple coalitions. The proposed coalitional methodology allows to solve the multiple local subproblems in parallel, hence reducing the overall computational burden, while guaranteeing the satisfaction of the operational constraints and without significantly compromising the overall performance. The effectiveness of proposed approach is shown through numerical simulations of a 10- and 100-loop version of the ACUREX solar collector field of Plataforma Solar de Almería, Spain.Peer ReviewedPostprint (published version

Data-driven control of multi-tank water systems : centralized and decentralized approaches with reinforcement learning

"Este trabajo investiga el control basado en datos de sistemas de tanques de agua con dinámica acoplada no lineal. Dichas dinámicas usualmente dificultan el diseño analítico de los controladores basados en modelos y requieren modelos dinámicos simplificados que ignoran la mayoría de los comportamientos no lineales del sistema. Como una forma de aliviar las dificultades de diseño y evitar simplificaciones de modelado, en este trabajo diseñamos métodos de aprendizaje por refuerzo (RL), centralizados y descentralizados, y métodos basados en datos para controlar sistemas de tanques de agua interconectados que son relevantes para el control de procesos industriales. En particular, estudiamos tres estructuras actor crítico y las aplicamos en un método del estado del arte de RL." -- Tomado del Formato de Documento de Grado"This work investigates the data-driven control of water-tank systems with nonlinear coupled dynamics. Such dynamics usually harden the analytic design of model-based controllers, and require simplified dynamical models that ignore most of the nonlinear behaviors of the system. As a way to alleviate the design difficulties and avoid modelling simplifications, we design centralized and decentralized reinforcement learning (RL) and data-driven methods to control interconnected water-tank systems relevant for industrial process control. In particular, we study three actor-critic structures and apply them on state-of-the-art RL methods." -- Tomado del Formato de Documento de GradoMagíster en Ingeniería Electrónica y de ComputadoresMaestrí

Distributed nash equilibrium seeking in strongly contractive aggregative population games

This paper addresses the problem of distributed Nash equilibrium (NE) seeking in strongly contractive aggregative multi-population games subject to partialdecision information. In particular, we consider the scenario where the so-called payoff providers of the multiple populations communicate through a possibly noncomplete network, and we formulate some consensus-like dynamics for the payoff providers to distributedly compute their payoff signals using local information only. Moreover, by exploiting the notions of d-passivity and d-antipassivity, we provide a unified analysis for several classes of evolutionary game dynamics. As the main contributions, we provide sufficient conditions to guarantee the d-antipassivity of a class of continuous-time dynamical systems, and we exploit such results to design distributed NE seeking dynamics for strongly contractive aggregative population games, as well as for a class of merely contractive aggregative population games. To the best of our knowledge, this is the first paper to consider the problem of distributed NE seeking for such classes of population games and from a unifying passivity-based perspective.This research has been supported by the projects PID2020-115905RB-C21 (LBEST) and TED2021-129927B-I00 (MASHED) funded by MCIN/AEI /10.13039/501100011033, and by the project BPIN2021000100499 funded by CTeI-SGR and MinCiencias,Colombia.Peer ReviewedPostprint (published version

Decentralized charging coordination of electric vehicles under feeder capacity constraints

As an envisioned technology for future smart city networks, this paper studies the real-time decentralized charging coordination of a fleet of plug-in electric vehicles (PEVs) under feeder capacity constraints. In particular, inspired by some ideas in the field of population games and payoff dynamics models, we propose a novel form of continuous-time primal-dual gradient dynamics and develop a real-time control method for the charging coordination of PEVs in smart city networks. The proposed method is able to coordinate the charging profiles of multiple PEVs in a decentralized fashion under a general convex optimization objective, and guarantees the satisfaction of the operational constraints of the PEVs and the feeder lines of the distribution network for all times. The optimality and asymptotic stability of the proposed dynamics are formally proven, and the advantages of the proposed method are illustrated through numerical simulations considering a fleet with several PEVs.The work of Juan Martinez-Piazuelo was supported in part by the Universitat Politècnica de Catalunya and in part by Banco Santander under Grant FPI-UPC. The work of Nicanor Quijano was supported by the U.K.-PACT Project (2019–2021), systemic perspectives on low-carbon cities in Colombia—An integrated urban modeling approach for policy and regulatory analysis. This work was supported by Project PID2020-115905RB-C21 (L-BEST) funded by MCIN/ AEI /10.13039/501100011033.Peer ReviewedPostprint (author's final draft

Nash equilibrium seeking in full-potential population games under capacity and migration constraints

This brief proposes a novel decision-making model for generalized Nash equilibrium seeking in the context of full-potential population games under capacity and migration constraints. The capacity constraints restrict the mass of players that are allowed to simultaneously play each strategy of the game, while the migration constraints introduce a networked interaction structure among the players and rule the strategic switches that players can make. In this brief, we consider both decoupled capacity constraints regarding individual strategies, as well as coupled capacity constraints regarding disjoint groups of strategies. As main technical contributions, we prove that the proposed decision-making protocol guarantees the forward time invariance of the feasible set, and we provide sufficient conditions on the connectivity level of the migration graph to guarantee the asymptotic stability of the set of generalized Nash equilibria of the underlying game when the game is a full-potential population game with concave potential function. Furthermore, we also provide an alternative discrete-time analysis of the proposed evolutionary game dynamics, which allows us to formulate a population-game-inspired distributed optimization algorithm that guarantees the hard satisfaction of the constraints over all iterations. Finally, the theoretical results are validated numerically on a constrained networked congestion game.Juan Martinez-Piazuelo gratefully acknowledges the Universitat Politècnica de Catalunya and Banco Santander for the financial support of his predoctoral grant FPI-UPC. In addition, the authors would like to thank the project PID2020-115905RB-C21 (L-BEST) funded by MCIN/ AEI /10.13039/501100011033 for supporting this research.Peer ReviewedPreprin

On distributed nash equilibrium seeking in a class of contractive population games

© 2022 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.In this paper, we consider the framework of population games and evolutionary dynamics. Based on such a framework, we formulate a novel approach for distributed Nash equilibrium seeking under partial-decision information for a class of evolutionary dynamics and a family of contractive population games. As the main contribution, we provide sufficient conditions to guarantee the asymptotic stability of the set of Nash equilibria of the underlying game. To the best of our knowledge, this is the first paper to address the problem of distributed Nash equilibrium seeking under partial-decision information in the aforementioned context of population games and evolutionary dynamics.The authors would like to thank the project PID2020-115905RB-C21 (L-BEST) funded by MCIN/AEI /10.13039/501100011033 for supporting this research.Peer ReviewedPostprint (author's final draft

A payoff dynamics model for generalized Nash equilibrium seeking in population games

This paper studies the problem of generalized Nash equilibrium seeking in population games under general affine equality and convex inequality constraints. In particular, we design a novel payoff dynamics model to steer the decision-making agents to a generalized Nash equilibrium of the underlying game, i.e., to a self-enforceable state where the constraints are satisfied and no agent has incentives to unilaterally deviate from her selected strategy. Moreover, using Lyapunov stability theory, we provide sufficient conditions to guarantee the asymptotic stability of the corresponding equilibria set in stable population games. Auxiliary results characterizing the properties of the equilibria set are also provided for general continuous population games. Furthermore, our theoretical developments are numerically validated on a Cournot game considering various market-related and production-related constraints.Juan Martinez-Piazuelo gratefully acknowledges the Universitat Politècnica de Catalunya, Spain and Banco Santander, Spain for the financial support of his predoctoral grant FPI-UPC, Spain . In addition, the authors would like to thank the project PID2020-115905RB-C21 (L-BEST) funded by MCIN/ AEI /10.13039/501100011033 for supporting this research. Finally, Nicanor Quijano would like to thank the UK-PACT Project (2019-2021), Systemic perspectives on low-carbon cities in Colombia – An integrated urban modelling approach for policy and regulatory analysis.Peer ReviewedPostprint (published version