On the Consensus Performance of Multi-Layered MASs with Various Graph Parameters—From the Perspective of Cardinalities of Vertex Sets
This work studies the first-order coherence of noisy multi-agent networks with multi-layered structures. The coherence, which is a sort of performance index of networks, can be seen as a sort of measurement for a system’s robustness. Graph operations are applied to design the novel multi-layered net...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-12-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/1/40 |
| _version_ | 1797443000235720704 |
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| author | Da Huang Zhiyong Yu |
| author_facet | Da Huang Zhiyong Yu |
| author_sort | Da Huang |
| collection | DOAJ |
| description | This work studies the first-order coherence of noisy multi-agent networks with multi-layered structures. The coherence, which is a sort of performance index of networks, can be seen as a sort of measurement for a system’s robustness. Graph operations are applied to design the novel multi-layered networks, and a graph spectrum approach, along with analysis methods, is applied to derive the mathematical expression of the coherence, and the corresponding asymptotic results on the performance index have been obtained. In addition, the coherence of these non-isomorphic multi-layered networks with three different graph parameters are compared and analyzed. We find that, when the cardinalities of the vertex sets of corresponding counterpart layers are the same, the multi-layered topology class with a balanced, complete, multi-partite structure has the best robustness of all the considered networks, if the sufficient conditions for the node-related parameters hold. Finally, simulations are given to verify the asymptotic results. |
| first_indexed | 2024-03-09T12:49:46Z |
| format | Article |
| id | doaj.art-2f140b641d29459d9910d411de3646c8 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T12:49:46Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-2f140b641d29459d9910d411de3646c82023-11-30T22:07:23ZengMDPI AGEntropy1099-43002022-12-012514010.3390/e25010040On the Consensus Performance of Multi-Layered MASs with Various Graph Parameters—From the Perspective of Cardinalities of Vertex SetsDa Huang0Zhiyong Yu1Department of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, ChinaCollege of Mathematics and System Science, Xinjiang University, Urumqi 830017, ChinaThis work studies the first-order coherence of noisy multi-agent networks with multi-layered structures. The coherence, which is a sort of performance index of networks, can be seen as a sort of measurement for a system’s robustness. Graph operations are applied to design the novel multi-layered networks, and a graph spectrum approach, along with analysis methods, is applied to derive the mathematical expression of the coherence, and the corresponding asymptotic results on the performance index have been obtained. In addition, the coherence of these non-isomorphic multi-layered networks with three different graph parameters are compared and analyzed. We find that, when the cardinalities of the vertex sets of corresponding counterpart layers are the same, the multi-layered topology class with a balanced, complete, multi-partite structure has the best robustness of all the considered networks, if the sufficient conditions for the node-related parameters hold. Finally, simulations are given to verify the asymptotic results.https://www.mdpi.com/1099-4300/25/1/40multi-agent systems (MASs)consensusmulti-partite graphmultilayered networksLaplacian spectrum |
| spellingShingle | Da Huang Zhiyong Yu On the Consensus Performance of Multi-Layered MASs with Various Graph Parameters—From the Perspective of Cardinalities of Vertex Sets Entropy multi-agent systems (MASs) consensus multi-partite graph multilayered networks Laplacian spectrum |
| title | On the Consensus Performance of Multi-Layered MASs with Various Graph Parameters—From the Perspective of Cardinalities of Vertex Sets |
| title_full | On the Consensus Performance of Multi-Layered MASs with Various Graph Parameters—From the Perspective of Cardinalities of Vertex Sets |
| title_fullStr | On the Consensus Performance of Multi-Layered MASs with Various Graph Parameters—From the Perspective of Cardinalities of Vertex Sets |
| title_full_unstemmed | On the Consensus Performance of Multi-Layered MASs with Various Graph Parameters—From the Perspective of Cardinalities of Vertex Sets |
| title_short | On the Consensus Performance of Multi-Layered MASs with Various Graph Parameters—From the Perspective of Cardinalities of Vertex Sets |
| title_sort | on the consensus performance of multi layered mass with various graph parameters from the perspective of cardinalities of vertex sets |
| topic | multi-agent systems (MASs) consensus multi-partite graph multilayered networks Laplacian spectrum |
| url | https://www.mdpi.com/1099-4300/25/1/40 |
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