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2015 | 25 | 2 | 353-360
Tytuł artykułu

A generalization of the graph Laplacian with application to a distributed consensus algorithm

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In order to describe the interconnection among agents with multi-dimensional states, we generalize the notion of a graph Laplacian by extending the adjacency weights (or weighted interconnection coefficients) from scalars to matrices. More precisely, we use positive definite matrices to denote full multi-dimensional interconnections, while using nonnegative definite matrices to denote partial multi-dimensional interconnections. We prove that the generalized graph Laplacian inherits the spectral properties of the graph Laplacian. As an application, we use the generalized graph Laplacian to establish a distributed consensus algorithm for agents described by multi-dimensional integrators.
Rocznik
Tom
25
Numer
2
Strony
353-360
Opis fizyczny
Daty
wydano
2015
otrzymano
2014-01-06
poprawiono
2014-07-07
Twórcy
  • Department of Mathematical Sciences, Shibaura Institute of Technology, Saitama 337-8570, Japan
Bibliografia
  • Bauer, P.H. (2008). New challenges in dynamical systems: The networked case, International Journal of Applied Mathematics and Computer Science 18(3): 271-277, DOI: 10.2478/v10006-008-0025-8.
  • Cai, K. and Ishii, H. (2012). Average consensus on digraphs, Automatica general strongly connected 48(11): 2750-2761.
  • Fax, J.A. and Murray, R.M. (2004). Information flow and cooperative control of vehicle formations, IEEE Transactions on Automatic Control 49(9): 1465-1476.
  • Gantmacher, F.R. (1959). The Theory of Matrices, Chelsea, New York, NY.
  • Jadbabaie, A., Lin, J. and Morse, A.S. (2003). Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transactions on Automatic Control 48(6): 988-1001.
  • Khalil, H.K. (2002). Nonlinear Systems, Second Edition, Prentice Hall, Englewood Cliffs, NJ.
  • Mohar, B. (1991). The Laplacian spectrum of graphs, in Y. Alavi, G. Chartrand, O. Ollermann and A. Schwenk (Eds.), Graph Theory, Combinatorics, and Applications, Wiley, New York, NY.
  • Moreau, L. (2005). Stability of multi-agent systems with time-dependent communication links, IEEE Transactions on Automatic Control 50(2): 169-182.
  • Olfati-Saber, R., Fax, J.A. and Murray, R.M. (2007). Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE 95(1): 215-233.
  • Priolo, A., Gasparri, A., Montijano, E. and Sagues, C. (2014). A distributed algorithm for average consensus on strongly connected weighted digraphs, Automatica 50(3): 946-951.
  • Ren, W. and Beard, R.W. (2005). Consensus seeking in multi-agent systems under dynamically changing interaction topologies, IEEE Transactions on Automatic Control 50(5): 655-661.
  • Shamma, J. (2008). Cooperative Control of Distributed MultiAgent Systems, Wiley, New York, NY.
  • Vicsek, T., Czirok, A., Ben-Jacob, E., Cohen, I. and Shochet, O. (1995). Novel type of phase transition in a system of self-driven particles, Physical Review Letters 75(6): 1226-1229.
  • Zhai, G., Okuno, S., Imae, J. and Kobayashi, T. (2009). A matrix inequality based design method for consensus problems in multi-agent systems, International Journal of Applied Mathematics and Computer Science 19(4): 639-646, DOI: 10.2478/v10006-009-0051-1.
  • Zhai, G., Takeda, J., Imae, J. and Kobayashi, T. (2010). Towards consensus in networked nonholonomic systems, IET Control Theory & Applications 4(10): 2212-2218.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv25i2p353bwm
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