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Robust synchronization of dynamical networks with compensation of disturbances

  • Robust and Adaptive Systems
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Abstract

In this paper, a robust output control scheme is proposed for a linear dynamical network such that every its local subsystem is described by a linear differential equation with a priori unknown parameters. The network is subject to unknown exogenous bounded disturbances. The considerations are based on the introduction of a directed graph with vertices associated with the corresponding nodes of the network. An algorithm is proposed which ensures the synchronization of the network along with the compensation of the unknown disturbances with required accuracy. It is shown that the proposed scheme also remains valid for a network associated with an undirected graph. The theoretical results are illustrated via a numerical example of a network with four nodes.

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References

  1. Yoshioka, C. and Namerikawa, T., Observed-based Consensus Control Strategy for Multi-Agent System with Communication Time Delay, Proc. 17th IEEE Int. Conf. Control Appl., San Antonio, 2008, pp. 1037–1042.

  2. Liu, Y., Jia, Y., Du, J., and Shiying, Y., Dynamic Output Feedback Control for Consensus of Multi-Agent Systems: An H ∞ Approach, Proc. Am. Control Conf., St. Louis, 2009, pp. 4470–4475.

  3. Dzhunusov, I.A. and Fradkov, A.L., Output Synchronization in Networks of Linear Plants, in Proc. XI Int. Conf. “Stability and Oscillations of Nonlinear Control Systems,” Moscow: Inst. Probl. Upravlen., 2010, pp. 1–2.

    Google Scholar 

  4. Scardovi, L. and Sepulchre, R., Synchronization in Networks of Identical Linear Systems, Automatica, 2009, vol. 45, pp. 2557–2562.

    Article  MATH  Google Scholar 

  5. Xie, G., Liu, H., Wang, L., and Jia, Y., Consensus in Networked Multi-Agent Systems via Sampled Sontrol: Switching Topology Case, Proc. Am. Control Conf., St. Louis, 2009, pp. 4525–4530.

  6. Ren, W. and Beard, R.W., Consensus Seeking in Multiagent Systems under Dynamically Changing Interaction Topologies, IEEE Trans. Automat. Control, 2005, vol. 50, no. 5, pp. 655–661.

    Article  MathSciNet  Google Scholar 

  7. Fradkov, A.L., Quadratic Lyapunov Functions in Adaptive Stabilization of Linear Dynamical Plants, Sib. Mat. Zh., 1976, no. 2, pp. 436–446.

  8. Agaev, R.P. and Chebotarev, P.Yu., The Matrix of Maximum Out Forests of a Digraph and Its Applications, Autom. Remote Control, 2000, vol. 61, no. 9, part 1, pp. 1424–1450.

    MATH  MathSciNet  Google Scholar 

  9. Tsykunov, A.M., Robust Control Algorithms with Compensation of Bounded Perturbations, Autom. Remote Control, 2007, vol. 68, no. 7, pp. 1213–1224.

    Article  MATH  MathSciNet  Google Scholar 

  10. Godsil, C. and Royle, G., Algebraic Graph Theory, New York: Springer-Verlag, 2001.

    Book  MATH  Google Scholar 

  11. Fradkov, A.L., Kiberneticheskaya fizika: principy i primery (Cybernetical Physics: Principles and Examples), St. Petersburg: Nauka, 2003.

    Google Scholar 

  12. Atassi, A.N. and Khalil, H.K., A Separation Principle for the Stabilization of a Class of Nonlinear Systems, IEEE Trans. Automat. Control, 1999, vol. 44, no. 9, pp. 1672–1687.

    Article  MATH  MathSciNet  Google Scholar 

  13. Lancaster, P., Theory of Matrices, New York: Academic, 1969. Translated under the title Teoriya matrits, Moscow: Nauka, 1973.

    MATH  Google Scholar 

  14. Brusin, V.A., On a Class of Singularly Disturbed Adaptive Systems. I, Autom. Remote Control, 1995, vol. 56, no. 4, part 2, pp. 552–559.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

    I. B. Furtat

  2. Astrakhan State Technical University, Astrakhan, Russia

    I. B. Furtat

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  1. I. B. Furtat
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Original Russian Text © I.B. Furtat, 2011, published in Avtomatika i Telemekhanika, 2011, No. 12, pp. 104–114.

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Furtat, I.B. Robust synchronization of dynamical networks with compensation of disturbances. Autom Remote Control 72, 2516–2526 (2011). https://doi.org/10.1134/S0005117911120071

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