Open AccessSynchronization of dynamical systems on Riemannian manifolds by an extended PID-type control theory: Numerical evaluation
Author(s) -
Simone Fiori,
Italo Cervigni,
Mattia Ippoliti,
Claudio Menotta
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2022047
Subject(s) - synchronization (alternating current) , pid controller , control theory (sociology) , scheme (mathematics) , dynamical systems theory , manifold (fluid mechanics) , computer simulation , mathematics , computer science , controller (irrigation) , control (management) , topology (electrical circuits) , control engineering , mathematical analysis , simulation , physics , engineering , artificial intelligence , temperature control , mechanical engineering , combinatorics , quantum mechanics , agronomy , biology
The present document outlines a non-linear control theory, based on the PID regulation scheme, to synchronize two second-order dynamical systems insisting on a Riemannian manifold. The devised extended PID scheme, referred to as M-PID, includes an unconventional component, termed 'canceling component', whose purpose is to cancel the natural dynamics of a system and to replace it with a desired dynamics. In addition, this document presents numerical recipes to implement such systems, as well as the devised control scheme, on a computing platform and a large number of numerical simulation results focused on the synchronization of Duffing-like non-linear oscillators on the unit sphere. Detailed numerical evaluations show that the canceling contribution of the M-PID control scheme is not critical to the synchronization of two oscillators, however, it possesses the beneficial effect of speeding up their synchronization. Simulation results obtained in non-ideal conditions, namely in the presence of additive disturbances and delays, reveal that the devised synchronization scheme is robust against high-frequency additive disturbances as well as against observation delays.