Optimization of a control law to synchronize first-order dynamical systems on Riemannian manifolds by a transverse component

Abstract

<p style='text-indent:20px;'>The present paper builds on the previous contribution by the second author, S. Fiori, <i>Synchronization of first-order autonomous oscillators on Riemannian manifolds</i>, Discrete and Continuous Dynamical Systems – Series B, Vol. 24, No. 4, pp. 1725 – 1741, April 2019. The aim of the present paper is to optimize a previously-developed control law to achieve synchronization of first-order non-linear oscillators whose state evolves on a Riemannian manifold. The optimization of such control law has been achieved by introducing a transverse control field, which guarantees reduced control effort without affecting the synchronization speed of the oscillators. The developed non-linear control theory has been analyzed from a theoretical point of view as well as through a comprehensive series of numerical experiments.</p>

Kuramoto Model with Delay: The Role of the Frequency Distribution

“…Other types of generalized Kuramoto models were studied as well, including timedependent [8,32,33], adaptive [34][35][36][37][38] and memristive [39] coupling, including noise [26,27,40], non-harmonic coupling functions [41,42] and pulse coupling [43,44], systems on smooth manifolds [45][46][47], etc. Typically, the analytic study of the Kuramto model and its generalizations is performed in the thermodynamic limit when the number of units tends to infinity.…”