Journal
IEEE ACCESS
Volume 4, Issue -, Pages 2615-2620Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/ACCESS.2016.2570518
Keywords
Weighted average consensus; generalized consensus; finite-time; discrete-time; distributed algorithm
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Funding
- Science and Technology Commission of Shanghai Municipality through the Shanghai Pujiang Program [15PJ1408300]
- National Natural Science Foundation of China [11505127]
- Program for Young Excellent Talents in Tongji University [2014KJ036]
- Fundamental Research Funds for the Central Universities [0800219319]
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In this paper, the finite-time consensus for arbitrary undirected graphs is discussed. We develop a parametric distributed algorithm as a function of a linear operator defined on the underlying graph and provide a necessary and sufficient condition guaranteeing weighted average consensus in K steps, where K is the number of distinct eigenvalues of the underlying operator. Based on the novel framework of generalized consensus meaning that consensus is reached only by a subset of nodes, we show that the finite time weighted average consensus can always be reached by a subset corresponding to the non-zero variables of the eigenvector associated with a simple eigenvalue of the operator. It is interesting that the final consensus state is shown to be freely adjustable if a smaller subset of consensus is admitted. Numerical examples, including synthetic and real-world networks, are presented to illustrate the theoretical results. Our approach is inspired by the recent method of successive nulling of eigenvalues by Safavi and Khan.
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