Minimum Data Rate for Exponential Stability of Networked Control Systems with Medium Access Constraints

Regular Paper Control Theory and Applications

Abstract

In this paper, we investigate the minimum data rate problem to guarantee the stability of the networked control systems (NCSs) suffered to the medium access constraints in the digital communication channel. Under the effect of medium access constraints, the data rate of each communication node switches between its pre-set value and zero according to the medium access status assigned by the scheduler. In order to guarantee the exponential stability, a new analysis approach combined with the average dwell time technique and entropy theory is established for the unstable scalar systems and vector systems to obtain the sufficient and necessary conditions for each subsystem. The obtained minimum data rate are related to the intrinsic entropy rate of the system and the duty factor allocated by the scheduler. An numerical example is given to illustrate the effectiveness of the designed minimum data rate for the NCSs which composed by a collection of subsystems.

Keywords

Average dwell time entropy theory medium access constraints minimum data rate networked control systems (NCSs) 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    P. Antsaklis and B. Baillieul, “Guest editorial special issue on networked control systems,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1421–1423, 2004. [click]MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    P. Antsaklis and B. Baillieul, “Special issue on technology of networked control systems,” Proceedings of the IEEE, vol. 95, no. 1, pp. 5–8, 2007.CrossRefGoogle Scholar
  3. [3]
    Y. Zhao and G. Guo, “Distributed tracking control of mobile sensor networks with intermittent communications,” Journal of the Franklin Institute, vol. 354, no. 8, pp. 3634–3647, 2017.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    Y. Zhao, L. Ding, G. Guo, and G. Yang, “Event-triggered average consensus for mobile sensor networks under a given energy budget,” Journal of the Franklin Institute, vol. 352, no. 12, pp. 5646–5660, 2015.MathSciNetCrossRefGoogle Scholar
  5. [5]
    M. Cloosterman, N. Wouw, M. Heemels, and H. Nijmeijer, “Stability of networked control systems with uncertain time-varying delays,” IEEE Transactions on Automatic Control, vol. 54, no. 7, pp. 1575–1580, 2009. [click]MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    B. Stefano, “Control over a communication channel with random noise and delays,” Automatica, vol. 44, no. 2, pp. 348–360, 2008.MathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    V. Gupta, B. Hassibi, and R. M. Murray, “Optimal LQG control across packet-dropping links,” System and Control Letters, vol. 56, no. 6, pp. 439–446, 2007. [click]MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    W. Zhang and L. Yu, “Output feedback stabilization of networked control systems with packet dropouts,” IEEE Transactions on Automatic Control, vol. 52, no. 9, pp. 1705–1710, 2007.MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    G. Nair and R. Evans, “Exponential stabilisability of finitedimensional linear systems with limited data rates,” Automatica, vol. 39, no. 4, pp. 585–593, 2003.MathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    S. Tatikonda and S. Mitter, “Control under communication constraints,” IEEE Transactions on Automatic Control, vol. 49, no. 7, pp. 1056–1068, 2004. [click]MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    N. Minero, M. Franceschetti, S. Dey, and G. Nair, “Data rate theorem for stabilization over time-varying feedback channels,” IEEE Transactions on Automatic Control, vol. 54, no. 2, pp. 243–255, 2009. [click]MathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    N. Martins, M. Dahleh, and N. Elia, “Feedback stabilization of uncertain systems in the presence of a direct link,” IEEE Transactions on Automatic Control, vol. 51, no. 3, pp. 438–447, 2006. [click]MathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    K. You and L. Xie, “Minimum data rate for mean square stabilization of discrete LTI systems over lossy channels,” IEEE Transactions on Automatic Control, vol. 55, no. 10, pp. 2373–2378, 2010.MathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    K. You and L. Xie, “Minimum data rate for mean square Stabilizability of linear systems with markovian packet losses,” IEEE Transactions on Automatic Control, vol. 56, no. 4, pp. 772–785, 2011. [click]MathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    W. Wong and R. Brockett, “Systems with finite communication bandwidth constraints-part I: state estimation problems,” IEEE Transactions on Automatic Control, vol. 42, no. 9, pp. 1294–1299, 1997. [click]MathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    W. Wong and R. Brockett, “Systems with finite communication bandwidth constraints. II. Stabilization with limited information feedback,” IEEE Transactions on Automatic Control, vol. 44, no. 5, pp. 1049–1053, 1999.MathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    G. Guo, Z. Lu, and Q. L. Han, “Control with Markov sensors/ actuators assignment,” IEEE Transactions on Automatic Control, vol. 57, no. 7, pp. 1799–1804, 2012. [click]MathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    H. Rehbinder and M. Sanfridson, “Scheduling of a limited communication channel for optimal control,” Automatica, vol. 40, no. 3, pp. 491–500, 2004. [click]MathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    L. Zhang and D. Hristu-Varsakelis, “Communication and control co-design for networked control systems,” Automatica, vol. 42, no. 6, pp. 953–958, 2006. [click]MathSciNetCrossRefMATHGoogle Scholar
  20. [20]
    G. C. Walsh, H. Ye, and L. G. Bushnell, “Stability analysis of networked control systems,” IEEE Transactions on Control Systems Technology, vol. 10, no. 3, pp. 438–446, 2002. [click]CrossRefGoogle Scholar
  21. [21]
    D. Nesic and A. R. Teel, “Input-output stability prop-erties of networked control systems,” IEEE Transactions on Automatic Control, vol. 49, no. 10, pp. 1650–1667, 2004. [click]MathSciNetCrossRefMATHGoogle Scholar
  22. [22]
    T. Cover and J. Thomas, Elements of Information Theory, Wiley-Interscience, New York, 2006MATHGoogle Scholar
  23. [23]
    R. Hon and C. Johson, Matix Analysis, Cambridge University Press, U. K., 1995.Google Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Information and EngineeringDalian UniversityDalianChina
  2. 2.State Key Laboratory of Synthetical Automation for Industrial ProcessNortheastern UniversityShenyangChina
  3. 3.School of Control EngineeringNortheastern University at QinhuangdaoQinhuangdaoChina

Personalised recommendations