Academic Journal
Speeding up finite-time consensus via minimal polynomial of a weighted graph — A numerical approach: Speeding up finite-time consensus via minimal polynomial of a weighted graph -- a numerical approach
| Title: | Speeding up finite-time consensus via minimal polynomial of a weighted graph — A numerical approach: Speeding up finite-time consensus via minimal polynomial of a weighted graph -- a numerical approach |
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| Authors: | Zheming Wang, Chong Jin Ong |
| Source: | Automatica. 93:415-421 |
| Publication Status: | Preprint |
| Publisher Information: | Elsevier BV, 2018. |
| Publication Year: | 2018 |
| Subject Terms: | 0209 industrial biotechnology, Applications of graph theory, Agent technology and artificial intelligence, rank minimization, Systems and Control (eess.SY), 02 engineering and technology, Decentralized systems, Electrical Engineering and Systems Science - Systems and Control, consensus algorithm, Discrete-time control/observation systems, minimal polynomial, 0203 mechanical engineering, Large-scale systems, FOS: Electrical engineering, electronic engineering, information engineering, Laplacian matrix, Computational methods in systems theory |
| Description: | Reaching consensus among states of a multi-agent system is a key requirement for many distributed control/optimization problems. Such a consensus is often achieved using the standard Laplacian matrix (for continuous system) or Perron matrix (for discrete-time system). Recent interest in speeding up consensus sees the development of finite-time consensus algorithms. This work proposes an approach to speed up finite-time consensus algorithm using the weights of a weighted Laplacian matrix. 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. Several examples are provided to illustrate the effectiveness of the approach. |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 0005-1098 |
| DOI: | 10.1016/j.automatica.2018.03.067 |
| DOI: | 10.48550/arxiv.1707.07380 |
| Access URL: | http://arxiv.org/pdf/1707.07380 http://arxiv.org/abs/1707.07380 https://zbmath.org/6957790 https://doi.org/10.1016/j.automatica.2018.03.067 http://ui.adsabs.harvard.edu/abs/2017arXiv170707380W/abstract https://dblp.uni-trier.de/db/journals/corr/corr1707.html#WangO17a https://www.sciencedirect.com/science/article/pii/S0005109818301626 https://arxiv.org/abs/1707.07380 https://dialnet.unirioja.es/servlet/articulo?codigo=6478696 |
| Rights: | Elsevier TDM arXiv Non-Exclusive Distribution |
| Accession Number: | edsair.doi.dedup.....9b4cad25a75e18cf1a78186e61d5c12a |
| Database: | OpenAIRE |
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