Boltzmann distributed replicator dynamics: population games in a microgrid context
type: Item
instance of: scholarly article
title: Boltzmann distributed replicator dynamics: population games in a microgrid context
zbMATH Open document ID: 1478.91017
author: Gustavo Chica-Pedraza
author: Eduardo Mojica-Nava
author: Ernesto Cadena-Muñoz
published in: Games
publication date: 2021-11-26T00:00:00Z
review text: Summary: Multi-agent systems (MAS) have been used to solve several optimization problems in control systems. MAS allow understanding the interactions between agents and the complexity of the system, thus generating functional models that are closer to reality. However, these approaches assume that information between agents is always available, which means the employment of a full-information model. Some tendencies have been growing in importance to tackle scenarios where information constraints are relevant issues. In this sense, game theory approaches appear as a useful technique that use a strategy concept to analyze the interactions of the agents and achieve the maximization of agent outcomes. In this paper, we propose a distributed control method of learning that allows analyzing the effect of the exploration concept in MAS. The dynamics obtained use Q-learning from reinforcement learning as a way to include the concept of exploration into the classic exploration-less replicator dynamics equation. Then, the Boltzmann distribution is used to introduce the Boltzmann-based distributed replicator dynamics as a tool for controlling agents behaviors. This distributed approach can be used in several engineering applications, where communications constraints between agents are considered. The behavior of the proposed method is analyzed using a smart grid application for validation purposes. Results show that despite the lack of full information of the system, by controlling some parameters of the method, it has similar behavior to the traditional centralized approaches.
Mathematics Subject Classification ID: 91A22
Mathematics Subject Classification ID: 93A16
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 7434007
zbMATH Keywords: Boltzmann distribution
zbMATH Keywords: economic dispatch problem
zbMATH Keywords: multi-agent systems
zbMATH Keywords: population dynamics
zbMATH Keywords: revision protocol
MaRDI profile type: Publication
full work available at URL: g12010008
OpenAlex ID: W3120994996
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DOI: 10.3390/G12010008
description: scientific article; zbMATH DE number 7434007