A stochastic approach to the synchronization of coupled oscillators

This paper deals with an optimal control problem associated with the Kuramoto model describing the dynamical behavior of a network of coupled oscillators. Our aim is to design a suitable control function allowing us to steer the system to a synchronized configuration in which all the oscillators are...

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Detalles Bibliográficos
Autores: Biccari, Umberto, Zuazua Iriondo, Enrique
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/698601
Acceso en línea:http://hdl.handle.net/10486/698601
https://dx.doi.org/10.3389/fenrg.2020.00115
Access Level:acceso abierto
Palabra clave:Coupled oscillators
Kuramoto model
Optimal control
Synchronization
Gradient descent
Random batch method
Matemáticas
Descripción
Sumario:This paper deals with an optimal control problem associated with the Kuramoto model describing the dynamical behavior of a network of coupled oscillators. Our aim is to design a suitable control function allowing us to steer the system to a synchronized configuration in which all the oscillators are aligned on the same phase. This control is computed via the minimization of a given cost functional associated with the dynamics considered. For this minimization, we propose a novel approach based on the combination of a standard Gradient Descent (GD) methodology with the recently-developed Random Batch Method (RBM) for the efficient numerical approximation of collective dynamics. Our simulations show that the employment of RBM improves the performances of the GD algorithm, reducing the computational complexity of the minimization process and allowing for a more efficient control calculation