Speeding up finite-time consensus via minimal polynomial of a weighted graph — A numerical approach
(2018) Automatica — Vol. 93, p. 415-421 (2018)
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- Authors
- Abstract
- This work proposes an approach to speed up finite-time consensus algorithm using the weights of a weighted Laplacian matrix. It is motivated by the need to reach consensus among states of a multi-agent system in a distributed control/optimization setting. The approach is an iterative procedure that finds a low-order minimal polynomial that is consistent with the topology of the underlying graph. In general, the lowest-order minimal polynomial achievable for a network system is an open research problem. This work proposes a numerical approach that searches for the lowest order minimal polynomial via a rank minimization problem using a two-step approach: the first being an optimization problem involving the nuclear norm and the second a correction step. Convergence of the algorithm is shown and effectiveness of the approach is demonstrated via several examples.
- Affiliations
National University of Singapore
Citations
Wang, Z., & Ong, C. J. (2018). Speeding up finite-time consensus via minimal polynomial of a weighted graph — A numerical approach. Automatica, 93, 415-421. https://doi.org/10.1016/j.automatica.2018.03.067 (Original work published 2018)