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Archivio digitale delle tesi discusse presso l’Università di Pisa

Tesi etd-03262017-210737


Tipo di tesi
Tesi di laurea magistrale
Autore
TIBERI, LORENZO
URN
etd-03262017-210737
Titolo
Cluster Synchronization in Networks of Kuramoto Oscillators: A Geometric Approach for Analysis and Control
Dipartimento
INGEGNERIA DELL'INFORMAZIONE
Corso di studi
INGEGNERIA ROBOTICA E DELL'AUTOMAZIONE
Relatori
relatore Prof. Innocenti, Mario
Parole chiave
  • clusterization
  • geometric control theory
  • nonlinear systems
  • optimization
  • oscillators
  • pattern formation
  • synchronization
Data inizio appello
04/05/2017
Consultabilità
Parziale
Data di rilascio
04/05/2087
Riassunto
Synchronization is crucial for the correct functionality of many natural and man-made complex systems. In
this work we characterize the formation of synchronization patterns in networks of Kuramoto oscillators. Specifically, we reveal conditions on the network weights and structure and on the oscillators’ natural frequencies that allow the phases of a group of oscillators to evolve cohesively, yet independently from the phases of oscillators in different clusters. Our conditions are applicable to general directed and weighted networks of heterogeneous oscillators. Surprisingly, although the oscillators exhibit nonlinear dynamics, our approach relies entirely on tools from linear algebra and graph theory. Further, we develop
a control mechanism to determine the smallest (as measured by the Frobenius norm) network perturbation to ensure the formation of a desired synchronization pattern. Our procedure allows to constrain the set of edges that can be modified, thus enforcing the sparsity structure of the network perturbation.
The results are validated through a set of numerical examples.
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