Non-delayed synchronization of non-autonomous dynamical systems on Riemannian manifolds and its applications
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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.
KeywordsControl theory Differential geometry Non-autonomous dynamical system Numerical calculus Riemannian manifold System synchronization
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.
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Conflicts of interest
The authors declare that they have no conflict of interest.
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