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arXiv · 1412.7011

Network Synchronization with Convexity

Guodong Shi·Alexandre Proutiere·Karl Henrik Johansson
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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.

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Guodong Shi, Alexandre Proutiere, Karl Henrik Johansson. 2014-12-22. Network Synchronization with Convexity. https://arxiv.org/abs/1412.7011

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