Control of synchronization phenomena in Complex Networks: The Kuramoto Model
The notion of Control in Complex Systems has started almost 60 years ago by Kalman. However, the results obtained were not sufficient for systems with complex topologies (Complex Networks) and non-linear dynamics. Thanks to many works and especially the one of Liu et.al. on 2011, the topic of Contro...
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| Formato: | tesis de maestría |
| Fecha de publicación: | 2022 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/368652 |
| Acesso em linha: | https://hdl.handle.net/2117/368652 |
| Access Level: | acceso abierto |
| Palavra-chave: | System theory Synchronization Kuramoto model Control of synchronization Explosive synchronization Lyapunov Sistemes de control Classificació AMS::93 Systems Theory Control::93A General Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Optimització |
| Resumo: | The notion of Control in Complex Systems has started almost 60 years ago by Kalman. However, the results obtained were not sufficient for systems with complex topologies (Complex Networks) and non-linear dynamics. Thanks to many works and especially the one of Liu et.al. on 2011, the topic of Control in Complex networks has returned to the forefront and has been studied intensively during the last decade. Big progress has been made, but still there are many different aspects unsolved in the area. Different notions like structural controllability or required energy to control a network have been imported, but a unifying framework between Complex Systems and Control Theory is still missing, as non-linearity, complexity and dimensionality make it difficult and very often infeasible to extract general and unifying conclusions about this kind of systems. In this work we explore the dynamical properties of the Kuramoto model, focusing the theoretical analysis on the Star-Graph topology taking into consideration the original Kuramoto model, as well as a perturbed expansion of it. Then, a candidate control Lyapunov function is proposed and together with the rest of the theoretical results, is validated by performing various numerical simulations and deploying Model Predictive Control for the controlled cases. |
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