Speeding up finite-time consensus via minimal polynomial of a weighted graph: A numerical approach

• Autores: Zheming Wang, Chong Jin Ong
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 93, 2018, págs. 415-421
• Idioma: inglés
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• Resumen

  • 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.