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Simultaneous Stability of Large-scale Systems via Distributed Control Network with Partial Information Exchange

  • Yanfei Zhu
  • Fuwen Yang
  • Chuanjiang Li
  • Yilian Zhang
Regular Papers Control Theory and Applications
  • 29 Downloads

Abstract

This paper is concerned with the simultaneous stability of the multi-mode large-scale systems composed of the interaction subsystems. A novel distributed control network consisting of multiple network-based controllers with the partial information exchange is adopted to simultaneously stabilize the large-scale systems in multiple operation modes. In the distributed control network (DCN), a partial state information exchange approach is developed to save the real-time communication and computation resources. To compensate for the effects of dynamic couplings between interaction subsystems, the designed controllers use both the local states and the neighbors’ partial information with packet dropouts for local feedback design. Then, a series of Lyapunov functions are constructed to derive a matrix-inequality-based sufficient condition for the existence of the desired controllers. Based on an orthogonal complement technique, the gains of the controllers in DCN are parameterized. The iterative algorithm for the solution of simultaneous stabilization problem is also developed. Finally, a numerical example is performed to show the relevant feature of the proposed method.

Keywords

Distributed control network multi-mode large-scale systems orthogonal complement partial state information simultaneous stability 

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References

  1. [1]
    R. D’Andrea and G. E. Dullerud, “Distributed control design for spatially interconnected systems,” IEEE Trans. on Automatic Control, vol. 48, no. 9, pp. 1478–1495, September 2003.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    H. Li, Q. H. Wu, and H. Huang, “Control of spatially interconnected systems with random communication losses,” Acta Automatica Sinica, vol. 36, no. 2, pp. 258–266, February 2010.MathSciNetGoogle Scholar
  3. [3]
    R. Saeks and J. Murray, “Fractional representation, algebraic geometry, and the simultaneous stabilization problem,” IEEE Trans. on Automatic Control, vol. 27, no. 4, pp. 895–903, August 1982.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    V. D. Blondel, Simultaneous Stabilization of Linear Systems, Springer-Verlag, New York, 1994.CrossRefMATHGoogle Scholar
  5. [5]
    V. D. Blondel and M. Gevers, “Simultaneous stabilizability of three linear systems is rationally undecidable,” Mathematics of Control, Signals, and Systems, vol. 6, no. 2, pp. 135–145, June 1993.MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    Y. Zhu and F. Yang, “Simultaneous H =H2 stabilization for chemical reaction systems based on orthogonal complement space,” International Journal of Automation and Computing, vol. 13, no. 1, pp. 19–30, February 2016.CrossRefGoogle Scholar
  7. [7]
    Y. Zhu and F. Yang, “Network-based simultaneous H stabilization for chemical reaction systems with multiple packet dropouts,” International Journal of Control, Automation and Systems, vol. 15, no. 1, pp. 104–112, February 2017.CrossRefGoogle Scholar
  8. [8]
    Z. Shu, J. Lam, and P. Li, “Simultaneous H stabilization via fixed-order controller: equivalence and computation,” Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, China, pp. 3244–3249, 2009.Google Scholar
  9. [9]
    H. B. Shi and L. Qi, “Static output feedback simultaneous stabilisation via coordinates transformations with free variables,” IET Control Theory and Applications, vol. 3, no. 8, pp. 1051–1058, August 2009.MathSciNetCrossRefGoogle Scholar
  10. [10]
    Y. Chen, T. Xu, C. Zeng, Z. Zhou, and Q. Zhang, “Simultaneous stabilization for uncertain descriptor systems with input saturation,” International Journal of Robust and Nonlinear Control, vol. 22, no. 17, pp. 1938–1951, November 2012.MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    L. Li, V. A. Ugrinovskii, and R. Orsi, “Decentralized robust control of uncertain Markov jump parameter systems via output feedback,” Automatica, vol. 13, no. 11, pp. 1932–1944, November 2007.MathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    Y. S. Huang and M. Wu, “Robust decentralized direct adaptive output feedback fuzzy control for a class of large-sale nonaffine nonlinear systems,” Information Sciences, vol. 181, no. 11, pp. 2392–2404, June 2011.MathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    J. H. van Schuppen, O. Boutin, P. L. Kempker, J. Komenda, T. Masopust, N. Pambakian, and A. C. M. Ran, “Control of distributed systems: tutorial and overview,” European Journal of Control, vol. 17, no. 5–6, pp. 579–602, 2011.MathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    C. Langbort, R. S. Chandra, and R. D’Andrea, “Distributed control design for systems interconnected over an arbitrary graph,” IEEE Trans. on Automatic Control, vol. 49, no. 9, pp. 1502–1519, September 2004.MathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    X. Yang, Y. Wang, and J. Xu, “Distributed stabilization of nonlinear networks with measurement output feedback,” Proceedings of the 33rd Chinese Control Conference, Nanjing, China, pp. 5863–5868, 2014.Google Scholar
  16. [16]
    F. Kazempour and J. Ghaisari, “The design of networked distributed sliding mode controllers with non-ideal links,” Journal of the Franklin Institute, vol. 349, no. 2, pp. 604–621, March 2012.MathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    F. Kazempour and J. Ghaisari, “Stability analysis of modelbased networked distributed control systems,” Journal of Process Control, vol. 23, no. 3, pp. 444–452, March 2013.CrossRefGoogle Scholar
  18. [18]
    N. Xia, F. Yang, and Q. L. Han, “Distributed eventtriggered networked set-membership filtering with partial information transmission,” IET Control Theory and Application, vol. 11, no. 2, pp. 155–163, January 2017.CrossRefGoogle Scholar
  19. [19]
    C. Huang, D. W. C. Ho, and J. Lu, “Partial-informationbased synchronization analysis for complex dynamical networks,” Journal of the Franklin Institute, vol. 352, no. 9, pp. 3458–3475, September 2015.MathSciNetCrossRefGoogle Scholar
  20. [20]
    C. Huang, D. W. C. Ho, and J. Lu, “Partial-informationbased distributed filtering in two-targets tracking sensor networks,” IEEE Trans. on Circuits and Systems I: Regular Papers, vol. 59, no. 4, pp. 820–832, April 2012.MathSciNetCrossRefGoogle Scholar
  21. [21]
    F. Yang, W. Wang, Y. Niu, and Y. Li, “Observer-based H control for networked systems with consecutive packet delays and losses,” International Journal of Control, Automation and Systems, vol. 8, no. 4, pp. 769–775, August 2010.CrossRefGoogle Scholar
  22. [22]
    F. Yang and Q. L. Han, “H control for networked systems with multiple packet dropouts,” Information Sciences, vol. 252, pp. 106–117, December 2013.MathSciNetCrossRefMATHGoogle Scholar
  23. [23]
    Y. Zhang, F. Yang, and Q. L. Han, “H control of LPV systems with randomly multi-step sensor delays,” International Journal of Control, Automation and Systems, vol. 12, no. 6, pp. 1207–1215, December 2014.CrossRefGoogle Scholar
  24. [24]
    A. E. Bouhtouri, D. Hinrichsen, and A. J. Pritchard, “H -type control for discrete-time stochastic systems,” International Journal of Robust and Nonlinear Control, vol. 9, no. 13, pp. 923–948, November 1999.MathSciNetCrossRefMATHGoogle Scholar
  25. [25]
    S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, Philadelphia, 1994.CrossRefMATHGoogle Scholar
  26. [26]
    Y. Wei, J. Qiu, H. R. Karimi, and M. Wang, “New results on H dynamic output feedback control for Markovian jump systems with time-varying delay and defective mode information,” Optimal Control Applications and Methods, vol. 35, no. 6, pp. 656–675, 2014.MathSciNetCrossRefMATHGoogle Scholar
  27. [27]
    Y. Wei, J. Qiu, and H. R. Karimi, “Reliable output feedback control of discrete-time fuzzy affine systems with actuator faults,” IEEE Trans. on Circuits and Systems-I: Regular Papers, vol. 64, no. 1, pp. 170–181, January 2017.CrossRefGoogle Scholar
  28. [28]
    J. Lofberg, “YALMIP: a toolbox for modeling and optimization in MATLAB,” Proceedings of the 2004 IEEE International Symposium on Computer Aided Control Systems Design, Taipei, Taiwan, pp. 284–289, 2004.Google Scholar
  29. [29]
    Y. Wei, J. Qiu, and H. R. Karimi, “Quantized H fltering for continuous-time Markovian jump systems with deficient mode information,” Asian Journal of Control, vol. 17, no. 5, pp. 1914–1923, September 2015.MathSciNetCrossRefMATHGoogle Scholar
  30. [30]
    Y. Wei, J. Qiu, H. R. Karimi, and M. Wang, “H model reduction for continuous-time Markovian jump systems with incomplete statistics of mode information,” International Journal of Systems Science, vol. 45, no. 7, pp. 1496–1507, 2014.MathSciNetCrossRefMATHGoogle Scholar
  31. [31]
    B. Shen, H. Tan, Z. Wang, and T. Huang, “Quantized/saturated control for sampled-data systems under noisy sampling intervals: a confluent vandermonde matrix approach,” IEEE Trans. on Automatic Control, vol. 62 no. 9, pp. 4753–4759, September 2017.MathSciNetCrossRefMATHGoogle 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

  • Yanfei Zhu
    • 1
  • Fuwen Yang
    • 2
  • Chuanjiang Li
    • 1
  • Yilian Zhang
    • 3
  1. 1.College of Information, Mechanical and Electrical EngineeringShanghai Normal UniversityShanghaiChina
  2. 2.Griffith School of EngineeringGriffith University, Gold Coast CampusNathanAustralia
  3. 3.Key Laboratory of Marine Technology and Control Engineering Ministry of CommunicationsShanghai Maritime UniversityShanghaiChina

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