The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Port-Hamiltonian Systems on Graphs
Open accessAbstract
In this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as port-Hamiltonian systems on open graphs. The basic idea is to associate with the incidence matrix of any directed graph a Dirac structure relating the flow and effort variables associated to the edges and vertices of the graph, and to formulate energy-storing or energy-dissipating relations between the flow and effort variables of the edges and the internal vertices. This allows for state variables associated to the edges and formalizes the interconnection of networks. Examples from different origins, such as consensus algorithms, that share the same structure are shown. It is shown how the identified Hamiltonian structure offers systematic tools for the analysis and control of the resulting dynamics.
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Citations
Cites
Consensus and Cooperation in Networked Multi-Agent Systems
Olfati-Saber, R., Fax, J. A., & Murray, R. M. (2007) · Proceedings of the IEEE · doi:10.1109/jproc.2006.887293 · Cited by 10,522 · cited 1×
“In the standard consensus algorithm (see, e.g., [25]), the vector x v of each follower agent v satisfies the dynamics (31) ˙ x v where g ( v,w ) > 0 denotes a certain positive-definite weight matrix associated to each edge.”
Synthesis of mechanical networks: the inerter
Smith, M. C. (2002) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2002.803532 · Cited by 1,828
Cited by
Port-Hamiltonian Systems Theory: An Introductory Overview
van der Schaft, A., & Jeltsema, D. (2014) · Foundations and Trends® in Systems and Control · doi:10.1561/2600000002 · Cited by 638
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Metadata
- Authors
- van der Schaft, A. J., & Maschke, B. M.
- Venue
- SIAM Journal on Control and Optimization
- Published
- 2013-01
- Volume
- 51
- Issue
- 2
- Pages
- 906-937
- ISSN
- 0363-0129 (ISSN-L)
- 1095-7138
- OpenAlex
- W2963870191
- Cited by
- 181
- References
- 2
- FWCI
- 22.80
- Type
- journal article
- Language
- en
- Open access
- green
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