Automation and Remote Control

, Volume 76, Issue 9, pp 1551–1565 | Cite as

Consensus in nonlinear stationary networks with identical agents

  • A. V. Proskurnikov
Nonlinear Systems


For the multiagent networks with arbitrary-order identical agents and nonlinear uncertain couplings, satisfying the sector inequalities consideration was given to the problem of reaching consensus (asymptotic synchronization) The network topology was assumed to be time-invariant. A frequency-domain consensus criterion extending the Popov criterion for the absolute stability of Lurie systems with one scalar-valued nonlinearity was proposed.


Remote Control Multiagent System Coupling Function Consensus Criterion Linear Coupling 
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.


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  1. 1.
    Agaev, R.P. and Chebotarev, P.Yu., Convergence and Stability in the Problem of Characteristic Coordination, Upravlen. Bol’shimi Sist., 2010, no. 30.1, pp. 470–505.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, 2011.zbMATHCrossRefGoogle Scholar
  4. 4.
    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
  5. 5.
    Reynolds, C.W., Flocks, Herds, and Schools: A Distributed Behavioral Model, Comput. Graphics, 1987, vol. 21, pp. 25–34.CrossRefGoogle Scholar
  6. 6.
    Bullo, F., Cortes, J., and Martinez, S., Distributed Control of Robotics Networks, Princeton: Princeton Univ. Press, 2009.CrossRefGoogle Scholar
  7. 7.
    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
  8. 8.
    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.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Shcherbakov, P.S., Formation Control: The Van Loan Scheme and Other Algorithms, Autom. Remote Control, 2011, vol. 72, no. 10, pp. 2210–2219.zbMATHCrossRefGoogle Scholar
  10. 10.
    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.zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    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.zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Amelina, N.O. and Fradkov, A.L., Approximate Consensus in the Dynamic Stochastic Network with Incomplete Information and Measurement Delays, Autom. Remote Control, 2012, vol. 73, no. 11, pp. 1765–1783.zbMATHMathSciNetCrossRefGoogle 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.zbMATHMathSciNetCrossRefGoogle 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.MathSciNetCrossRefGoogle Scholar
  15. 15.
    Wieland, P., Sepulchre, R., and Allgöwer, F., An Internal Model Principle is Necessary and Sufficient for Linear Output Synchronization, Automatica, 2011, vol. 47, pp. 1068–1074.zbMATHCrossRefGoogle Scholar
  16. 16.
    Strogatz, S., From Kuramoto to Crawford: Exploring the Onset of Synchronization in Populations of Coupled Oscillators, Physica D, 2000, no. 143, pp. 643–651.MathSciNetCrossRefGoogle Scholar
  17. 17.
    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.zbMATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    Fang, L. and Antsaklis, P., Asynchronous Consensus Protocols Using Nonlinear Paracontractions Theory, IEEE Trans. Autom. Control, 2008, vol. 53, no. 10, pp. 2351–2355.MathSciNetCrossRefGoogle Scholar
  19. 19.
    Miroshnik, I.V., Nikiforov, V.O., and Fradkov, A.L., Nelineinoe i adaptivnoe upravlenie slozhnymi dinamicheskimi sistemami (Nonlinear and Adaptive Control of Complex Dynamic Systems), St. Petersburg: Nauka, 2000.Google Scholar
  20. 20.
    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
  21. 21.
    Proskurnikov, A., Consensus in Switching Networks with Sectorial Nonlinear Couplings: Absolute Stability Approach, Automatica, 2013, vol. 49, no. 2, pp. 488–495.zbMATHMathSciNetCrossRefGoogle Scholar
  22. 22.
    Proskurnikov, A., Nonlinear Consensus Algorithms with Uncertain Couplings, Asian J. Control, 2014, vol. 16, no. 5, pp. 1277–1288.zbMATHMathSciNetCrossRefGoogle Scholar
  23. 23.
    Proskurnikov, A.V., Frequency-domain Criteria for Consensus in Multiagent Systems with Nonlinear Sector-shaped Couplings, Autom. Remote Control, 2014, vol. 75, no. 11, pp. 1982–1995.MathSciNetCrossRefGoogle Scholar
  24. 24.
    Gelig, A.Kh., Leonov, G.A., and Yakubovich, V.A., Ustoichivost’ nelineinykh sistem s needinstvennym sostoyaniem ravnovesiya (Stability of Nonlinear Systems with Nonunique Equilibrium), Moscow: Nauka, 1978.Google Scholar
  25. 25.
    Popov, V.M., Giperustoichivost’ avtomaticheskikh sistem (Hyperstability of Automatic Systems), Moscow: Nauka, 1970.Google Scholar
  26. 26.
    Ren, W., On Consensus Algorithms for Double-integrator Dynamics, IEEE Trans. Autom. Control, 2008, vol. 49, no. 9, pp. 1503–1509.CrossRefGoogle Scholar
  27. 27.
    Fiedler, M., Algebraic Connectivity of Graphs, Czech. Math. J., 1973, vol. 23, pp. 298–305.MathSciNetGoogle Scholar
  28. 28.
    Merris, R., Laplacian Matrices of Graphs: A Survey, Linear Algebra Appl., 1994, vol. 197, pp. 143–176.MathSciNetCrossRefGoogle Scholar
  29. 29.
    Lafferriere, G., Williams, A., Caughman, J., and Veerman, J.J.P., Decentralized Control of Vehicle Formations, Syst. Control Lett., 2005, vol. 54, pp. 899–910.zbMATHMathSciNetCrossRefGoogle Scholar
  30. 30.
    Zheng, Y. and Wang, L., Consensus of Heterogeneous Multi-agent Systems without Velocity Measurements, Int. J. Control, 2012, vol. 85, no. 7, pp. 906–914.zbMATHCrossRefGoogle Scholar
  31. 31.
    Yakubovich, V.A., Frequency Theorem in the Control Theory, Sib. Mat. Zh., 1973, vol. 14, no. 2, pp. 384–420.zbMATHCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Institute of Problems of Mechanical EngineeringRussian Academy of SciencesSt. PetersburgRussia
  3. 3.Mechanics and OpticsSt. Petersburg State National Research University of Information TechnologiesSt. PetersburgRussia

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