Network Synchronization with Convexity
Abstract
In this paper, we establish a few new synchronization conditions for complex networks with nonlinear and nonidentical self-dynamics with switching directed communication graphs. In light of the recent works on distributed sub-gradient methods, we impose integral convexity for the nonlinear node self-dynamics in the sense that the self-dynamics of a given node is the gradient of some concave function corresponding to that node. The node couplings are assumed to be linear but with switching directed communication graphs. Several sufficient and/or necessary conditions are established for exact or approximate synchronization over the considered complex networks. These results show when and how nonlinear node self-dynamics may cooperate with the linear diffusive coupling, which eventually leads to network synchronization conditions under relaxed connectivity requirements.
Keywords
Cite
@article{arxiv.1412.7011,
title = {Network Synchronization with Convexity},
author = {Guodong Shi and Alexandre Proutiere and Karl Henrik Johansson},
journal= {arXiv preprint arXiv:1412.7011},
year = {2015}
}
Comments
Based on our previous manuscript arXiv:1210.6685. SIAM Journal on Control and Optimization, in press 2016