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Nonlinear Dynamics

, Volume 94, Issue 4, pp 3077–3100 | Cite as

Non-delayed synchronization of non-autonomous dynamical systems on Riemannian manifolds and its applications

  • Simone Fiori
Original Paper
  • 54 Downloads

Abstract

The present paper aims at tackling the non-delayed synchronization of two first-order, non-autonomous dynamical systems whose state spaces are (curved) Riemannian manifolds. The present research endeavor borrows notions from system theory, differential geometry, control theory and numerical calculus to design a general synchronization theory and a set of numerical methods to implement the devised synchronization theory on a computing platform. The features of these synchronization algorithms are illustrated by means of five sets of numerical experiments including the synchronization of the attitude of a fleet of flying bodies and the secure transmission of a message by the modulation of a system-generated carrier.

Keywords

Control theory Differential geometry Non-autonomous dynamical system Numerical calculus Riemannian manifold System synchronization 

Notes

Acknowledgements

I wish to gratefully thank the anonymous reviewers, who contributed significantly to enrich the quality of the present paper by a number of interesting observation and suggestions.

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.

Supplementary material

Supplementary material 1 (mp4 3260 KB)

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria dell’InformazioneUniversità Politecnica delle MarcheAnconaItaly

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