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- Publisher Website: 10.1109/TNNLS.2021.3058184
- Scopus: eid_2-s2.0-85102307676
- PMID: 33646958
- WOS: WOS:000732273100001
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Article: Consensus of Positive Networked Systems on Directed Graphs
Title | Consensus of Positive Networked Systems on Directed Graphs |
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Authors | |
Keywords | Algebraic Riccati inequality (ARI) directed graphs networked systems positive consensus positive systems |
Issue Date | 2021 |
Publisher | IEEE. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=72 |
Citation | IEEE Transactions on Neural Networks and Learning Systems, 2021, Epub 2021-03-01 How to Cite? |
Abstract | This article addresses the distributed consensus problem for identical continuous-time positive linear systems with state-feedback control. Existing works of such a problem mainly focus on the case where the networked communication topologies are of either undirected and incomplete graphs or strongly connected directed graphs. On the other hand, in this work, the communication topologies of the networked system are described by directed graphs each containing a spanning tree, which is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains. Specifically, the problem involves complex eigenvalues, the Hurwitzness of complex matrices, and positivity constraints, which make analysis difficult in the Laplacian matrix. First, a necessary and sufficient condition for the consensus analysis of directed networked systems with positivity constraints is given, by using positive systems theory and graph theory. Unlike the general Riccati design methods that involve solving an algebraic Riccati equation (ARE), a condition represented by an algebraic Riccati inequality (ARI) is obtained for the existence of a solution. Subsequently, an equivalent condition, which corresponds to the consensus design condition, is derived, and a semidefinite programming algorithm is developed. It is shown that, when a protocol is solved by the algorithm for the networked system on a specific communication graph, there exists a set of graphs such that the positive consensus problem can be solved as well. |
Persistent Identifier | http://hdl.handle.net/10722/290593 |
ISSN | 2023 Impact Factor: 10.2 2023 SCImago Journal Rankings: 4.170 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Liu, JJ | - |
dc.contributor.author | Kwok, KW | - |
dc.contributor.author | Cui, Y | - |
dc.contributor.author | SHEN, J | - |
dc.contributor.author | Lam, J | - |
dc.date.accessioned | 2020-11-02T05:44:26Z | - |
dc.date.available | 2020-11-02T05:44:26Z | - |
dc.date.issued | 2021 | - |
dc.identifier.citation | IEEE Transactions on Neural Networks and Learning Systems, 2021, Epub 2021-03-01 | - |
dc.identifier.issn | 2162-237X | - |
dc.identifier.uri | http://hdl.handle.net/10722/290593 | - |
dc.description.abstract | This article addresses the distributed consensus problem for identical continuous-time positive linear systems with state-feedback control. Existing works of such a problem mainly focus on the case where the networked communication topologies are of either undirected and incomplete graphs or strongly connected directed graphs. On the other hand, in this work, the communication topologies of the networked system are described by directed graphs each containing a spanning tree, which is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains. Specifically, the problem involves complex eigenvalues, the Hurwitzness of complex matrices, and positivity constraints, which make analysis difficult in the Laplacian matrix. First, a necessary and sufficient condition for the consensus analysis of directed networked systems with positivity constraints is given, by using positive systems theory and graph theory. Unlike the general Riccati design methods that involve solving an algebraic Riccati equation (ARE), a condition represented by an algebraic Riccati inequality (ARI) is obtained for the existence of a solution. Subsequently, an equivalent condition, which corresponds to the consensus design condition, is derived, and a semidefinite programming algorithm is developed. It is shown that, when a protocol is solved by the algorithm for the networked system on a specific communication graph, there exists a set of graphs such that the positive consensus problem can be solved as well. | - |
dc.language | eng | - |
dc.publisher | IEEE. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=72 | - |
dc.relation.ispartof | IEEE Transactions on Neural Networks and Learning Systems | - |
dc.rights | IEEE Transactions on Neural Networks and Learning Systems. Copyright © IEEE. | - |
dc.rights | ©20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. | - |
dc.subject | Algebraic Riccati inequality (ARI) | - |
dc.subject | directed graphs | - |
dc.subject | networked systems | - |
dc.subject | positive consensus | - |
dc.subject | positive systems | - |
dc.title | Consensus of Positive Networked Systems on Directed Graphs | - |
dc.type | Article | - |
dc.identifier.email | Liu, JJ: liujinr@hku.hk | - |
dc.identifier.email | Kwok, KW: kwokkw@hku.hk | - |
dc.identifier.email | Lam, J: jlam@hku.hk | - |
dc.identifier.authority | Kwok, KW=rp01924 | - |
dc.identifier.authority | Lam, J=rp00133 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1109/TNNLS.2021.3058184 | - |
dc.identifier.pmid | 33646958 | - |
dc.identifier.scopus | eid_2-s2.0-85102307676 | - |
dc.identifier.hkuros | 318451 | - |
dc.identifier.volume | Epub 2021-03-01 | - |
dc.identifier.isi | WOS:000732273100001 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 2162-237X | - |