Network Synchronization with Convexity
Date
2015
Authors
Shi, Guodong
Proutiere, Alexandre
Johansson, Karl Henrik
Journal Title
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Volume Title
Publisher
Society for Industrial and Applied Mathematics
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 subgradient 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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Keywords
coupled oscillator, complex networks, synchronization, switching graphs
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SIAM Journal on Control and Optimization
Type
Journal article
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Open Access
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