Automation and Remote Control

, Volume 75, Issue 11, pp 1982–1995 | Cite as

Frequency-domain criteria for consensus in multiagent systems with nonlinear sector-shaped couplings

Robust and Adaptive Systems


Consideration was given to the distributed algorithms for consensus (synchronization) in the multiagent networks with identical agents of arbitrary order and unknown nonlinear couplings satisfying the sector inequalities or their multidimensional counterparts. The network topology may be unknown and varying in time. A frequency synchronization criterion was proposed which is a generalization of the circular criterion for absolute stability of the Lur’e systems.


Remote Control MULTIAGENT System Coupling Function Quadratic Constraint Consensus Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bullo, F., Cortes, J., and Martinez, S., Distributed Control of Robotics Networks, Princeton: Princeton Univ. Press, 2009.Google Scholar
  2. 2.
    Ren, W. and Beard, R., Distributed Consensus in Multi-Vehicle Cooperative Control: Theory and Applications, London: Springer, 2008.CrossRefGoogle Scholar
  3. 3.
    Ren, W. and Cao, W., Distributed Coordination of Multi-Agent Networks, London: Springer, 2011CrossRefMATHGoogle Scholar
  4. 4.
    Chopra, N. and Spong, M.W., Passivity-Based Control of Multi-Agent Systems, in Advances in Robot Control, Kawamura, S. and Svinin, M., Eds., Berlin: Springer, 2006, pp. 107–134.CrossRefGoogle Scholar
  5. 5.
    Shcherbakov, P.S., Formation Control: The Van Loan Scheme and Other Algorithms, Autom. Remote Control, 2011, vol. 72, no. 10, pp. 2210–2219.CrossRefMATHGoogle Scholar
  6. 6.
    Kvinto, Ya.I. and Parsegov, S.E., Equidistant Arrangement of Agents on Line: Analysis of the Algorithm and Its Generalization, Autom. Remote Control, 2012, vol. 73, no. 11, pp. 1784–1793.CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Morozov, Yu.V., Modification and Comparative Analysis of Smooth Control Laws for a Group of Agents, Autom. Remote Control, 2012, vol. 73, no. 11, pp. 1838–1851.CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Fax, J.A. and Murray, R.M., Information Flow and Cooperative Control of Vehicle Formations, IEEE Trans. Autom. Control, 2004, vol. 49, no. 9, pp. 1465–1476.CrossRefMathSciNetGoogle Scholar
  9. 9.
    Paley, D., Sepulchre, R., and Leonard, N.E., Stabilization of Planar Collective Motion with Limited Communication, IEEE Trans. Autom. Control, 2008, vol. 53, no. 6, pp. 706–719.MathSciNetGoogle Scholar
  10. 10.
    Tanner, H.G., Jadbabaie, A., and Pappas, G.J., Flocking in Fixed and Switching Networks, IEEE Trans. Autom. Control, 2007, vol. 52, no. 5, pp. 863–868.CrossRefMathSciNetGoogle Scholar
  11. 11.
    Agaev, R.P. and Chebotarev, P.Yu., Convergence and Stability in Problems of Coordination of Characteristics, Upravlen. Bol’shimi Sist., 2010, vol. 30, no. 1, pp. 470–505.Google Scholar
  12. 12.
    Olfati-Saber, R., Fax, J.A., and Murray, R.M., Consensus and Cooperation in Networked Multi-Agent Systems, Proc. IEEE, 2007, vol. 95, no. 1, pp. 215–233.CrossRefGoogle Scholar
  13. 13.
    Agaev, R.P. and Chebotarev, P.Yu., Coordination in Multiagent Systems and Laplacian Spectra of Digraphs, Autom. Remote Control, 2009, vol. 70, no. 3, pp. 469–483.CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Moreau, L., Stability of Multiagent Systems with Time-Dependent Communication Links, IEEE Trans. Autom. Control, 2005, vol. 50, no. 2, pp. 169–182.CrossRefMathSciNetGoogle Scholar
  15. 15.
    Wieland, P., Sepulchre, R., and Allgöwer, F., An Internal Model Principle is Necessary and Sufficient for Linear Output Synchronizationg, Automatica, 2011, vol. 47, pp. 1068–1074.CrossRefMATHGoogle Scholar
  16. 16.
    Chopra, N. and Spong, M.W., On Exponential Synchronization of Kuramoto Oscillators, IEEE Trans. Autom. Control, 2009, vol. 54, no. 2, pp. 353–357.CrossRefMathSciNetGoogle Scholar
  17. 17.
    Strogatz, S., From Kuramoto to Crawford: Exploring the Onset of Synchronization in Populations of Coupled Oscillators, Physica D, 2000, no. 143, pp. 643–651.Google Scholar
  18. 18.
    Lin, Z., Francis, B., and Maggiore, M., State Agreement for Continuous-Time Coupled Nonlinear Systems, SIAM J. Control Optim., 2007, vol. 46, no. 1, pp. 288–307.CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Fang, L. and Antsaklis, P., Asynchronous Consensus Protocols Using Nonlinear Paracontractions Theory, IEEE Trans. Autom. Control, 2008, vol. 53, no. 10, pp. 2351–2355.CrossRefMathSciNetGoogle Scholar
  20. 20.
    Opoitsev, V.I., Ravnovesie i ustoichivost’ v modelyakh kollektivnogo povedeniya (Equilibrium and Stability in Models of Collective Behavior), Moscow: Nauka, 1977.Google Scholar
  21. 21.
    Arcak, M., Passivity as a Design Tool for Group Coordination, IEEE Trans. Autom. Control, 2007, vol. 52, no. 8, pp. 1380–1390.CrossRefMathSciNetGoogle Scholar
  22. 22.
    Gelig, A.Kh., Leonov, G.A., and Yakubovich, V.A., Ustoichivost’ nelineinykh sistem s needinstvennym sostoyaniem ravnovesiya (Stability of Nonlinear Systems with Nonunique Equilibrium State), Moscow: Nauka, 1978.Google Scholar
  23. 23.
    Miroshnik, I.V., Nikiforov, V.O., and Fradkov, A.L., Nelineinoe i adaptivnoe upravlenie slozhnymi dinamicheskimi sistemami (Nonlinear and Adaptive Control of Complex Dynaic Systems), St. Petersburg: Nauka, 2000.Google Scholar
  24. 24.
    Dzhunusov, I.A. and Fradkov, A.L., Synchronization in Networks of Linear Agents with Output Feedbacks, Autom. Remote Control., 2011, vol. 72. no. 8, pp. 1615–1626.CrossRefMathSciNetGoogle Scholar
  25. 25.
    Fiedler, M., Algebraic Connectivity of Graphs, Czech. Math. J., 1973, vol. 23, pp. 298–305.MathSciNetGoogle Scholar
  26. 26.
    Olfati-Saber, R. and Murray, R.M., Consensus Problems in Networks of Agents with Switching Topology and Time-Delays, IEEE Trans. Autom. Control, 2004, vol. 49, no. 9, pp. 1520–1533.CrossRefMathSciNetGoogle Scholar
  27. 27.
    Merris, R., Laplacian Matrices of Graphs: A Survey, Linear Algebra Appl., 1994, vol. 197, pp. 143–176.CrossRefMathSciNetGoogle Scholar
  28. 28.
    Yakubovich, V.A., Frequency Theorem in the Control Theory, Sib. Mat. Zh., 1973, vol. 14, no. 2, pp. 384–420.CrossRefMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Institute of Problems of Mechanical EngineeringRussian Academy of SciencesSt. PetersburgRussia

Personalised recommendations