Open AccessPosted Content
On the stability of the Kuramoto model of coupled nonlinear oscillators
Reads0
Chats0
TLDR
In this article, the authors provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators and is applicable to oscillator networks of arbitrary interconnection topology with uncertain natural frequencies.Abstract:
We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary interconnection topology with uncertain natural frequencies. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value, the synchronized state is locally asymptotically stable, resulting in convergence of all phase differences to a constant value, both in the case of identical natural frequencies as well as uncertain ones. We further explain the behavior of the system as the number of oscillators grows to infinity.read more
Citations
More filters
Journal ArticleDOI
Consensus and Cooperation in Networked Multi-Agent Systems
TL;DR: A theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees is provided.
Journal ArticleDOI
Information consensus in multivehicle cooperative control
TL;DR: Theoretical results regarding consensus-seeking under both time invariant and dynamically changing communication topologies are summarized in this paper, where several specific applications of consensus algorithms to multivehicle coordination are described.
Journal ArticleDOI
Stability of multiagent systems with time-dependent communication links
TL;DR: It is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence, even for the simple models discussed in the present paper.
Proceedings ArticleDOI
A survey of consensus problems in multi-agent coordination
TL;DR: A survey of consensus problems in multi-agent cooperative control with the goal of promoting research in this area is provided in this paper, where theoretical results regarding consensus seeking under both time-invariant and dynamically changing information exchange topologies are summarized.
BookDOI
Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms
TL;DR: This self-contained introduction to the distributed control of robotic networks offers a broad set of tools for understanding coordination algorithms, determining their correctness, and assessing their complexity; and it analyzes various cooperative strategies for tasks such as consensus, rendezvous, connectivity maintenance, deployment, and boundary estimation.
References
More filters
Journal ArticleDOI
The Structure and Function of Complex Networks
TL;DR: Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
Journal ArticleDOI
Consensus problems in networks of agents with switching topology and time-delays
TL;DR: A distinctive feature of this work is to address consensus problems for networks with directed information flow by establishing a direct connection between the algebraic connectivity of the network and the performance of a linear consensus protocol.
Book
Algebraic Graph Theory
Chris Godsil,Gordon F. Royle +1 more
TL;DR: The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial.
Journal ArticleDOI
Coordination of groups of mobile autonomous agents using nearest neighbor rules
Ali Jadbabaie,Jie Lin,A.S. Morse +2 more
TL;DR: A theoretical explanation for the observed behavior of the Vicsek model, which proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
Journal ArticleDOI
Exploring complex networks
TL;DR: This work aims to understand how an enormous network of interacting dynamical systems — be they neurons, power stations or lasers — will behave collectively, given their individual dynamics and coupling architecture.