Synchronization of dynamical systems on Riemannian manifolds by an extended PID-type control theory: Numerical evaluation

<p style='text-indent:20px;'>The present document outlines a non-linear control theory, based on the PID regulation scheme, to synchronize two second-order dynamical systems insisting Riemannian manifold. The devised extended referred as M-PID, includes an unconventional component, termed 'canceling component', whose purpose is cancel natural dynamics of system and replace it with desired dynamics. In addition, this presents numerical recipes implement such systems, well computing platform large number simulation results focused synchronization Duffing-like oscillators unit sphere. Detailed evaluations show that canceling contribution M-PID scheme not critical oscillators, however, possesses beneficial effect speeding up their synchronization. Simulation obtained in non-ideal conditions, namely presence additive disturbances delays, reveal robust against high-frequency observation delays.</p>