Non-delayed synchronization of non-autonomous dynamical systems on Riemannian manifolds and its applications
- 113 Downloads
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.
Compliance with ethical standards
Conflicts of interest
The authors declare that they have no conflict of interest.
Supplementary material 1 (mp4 3260 KB)
- 5.Bloch, A.M.: Nonholonomic Mechanics and Control. Springer, Berlin (2000)Google Scholar
- 27.Seuret, A., Dimarogonas, D.V., Johansson, K.H.: Consensus under communication delays. In: Proceedings of the 47th IEEE Conference on Decision and Control (Cancun, Mexico, December 2008), pp. 4922–4927 (2009)Google Scholar
- 29.Stankovski, T.: Tackling the inverse problem for non-autonomous systems: application to the life sciences. In: Springer Theses. Springer (2014) ISBN: 9783319007526Google Scholar
- 30.Tyagi, A., Davis, J.W.: A recursive filter for linear systems on Riemannian manifolds. In: Proceedings of the 2008 IEEE conference on computer vision and pattern recognition (Anchorage, AK, June 2008) (2008)Google Scholar