Stochastic Stability of Discrete-Time Phase-Coupled Oscillators Over Uncertain and Random Networks

• 成果类型: Article
• 署名作者: Jafarian, Matin; Mamduhi, Mohammad H.; Johansson, Karl H.
• 署名单位: Delft University of Technology; Swiss Federal Institutes of Technology Domain; ETH Zurich; Royal Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3303102
• 发表日期: 2024
• 页码: 2915-2930
• 关键词: Markov processes; Nonlinear systems; Stochastic systems; synchronization of coupled oscillators

摘要

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 $2\pi$-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 Erd & ouml;s-R & eacute;nyi 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.