Stochastic Stability of Discrete-time Phase-coupled Oscillators over Uncertain and Random Networks

Stochastic Stability of Discrete-time Phase-coupled Oscillators over Uncertain and Random Networks

Jafarian, M. (TU Delft Team Matin Jafarian)
Mamduhi, Mohammad H. (ETH Zürich)
Johansson, Karl H. (KTH Royal Institute of Technology)

2023

This article studies stochastic relative phase stability, i.e., stochastic phase-cohesiveness, of discrete-time phase-coupled oscillators. The stochastic phase-cohesiveness in two types of networks is studied. First, we consider oscillators coupled with 2π-periodic odd functions over underlying undirected graphs subject to both multiplicative and additive stochastic uncertainties. We prove stochastic phase-cohesiveness of the network with respect to two specific, namely, in-phase and antiphase, sets by deriving sufficient coupling conditions. We show the dependency of these conditions on the size of the mean values of additive and multiplicative uncertainties, as well as the sign of the mean values of multiplicative uncertainties. Furthermore, we discuss the results under a relaxation of the odd property of the coupling function. Second, we study an uncertain network in which the multiplicative uncertainties are governed by the Bernoulli process representing the well-known Erdös-Rényi network. We assume constant exogenous frequencies and derive sufficient conditions for achieving both stochastic phase-cohesive and phase-locked solutions, i.e., stochastic phase-cohesiveness with respect to the origin. For the latter case, where identical exogenous frequencies are assumed, we prove that any positive probability of connectivity leads to phase-locking. Thorough analyses are provided, and insights obtained from stochastic analysis are discussed, along with numerical simulations to validate the analytical results.

Couplings
Markov processes
Nonlinear systems
Oscillators
Stability analysis
Stochastic processes
Stochastic systems
Synchronization
Uncertainty

http://resolver.tudelft.nl/uuid:6c672692-89d3-4ec7-96d1-a084a27c701c

https://doi.org/10.1109/TAC.2023.3303102

2024-03-07

0018-9286

IEEE Transactions on Automatic Control, 69 (5), 2915-2930

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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© 2023 M. Jafarian, Mohammad H. Mamduhi, Karl H. Johansson