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Robust \(\mathcal{H}_{\infty}\) State Feedback Control of Networked Control Systems with Congestion Control

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Abstract

This paper examines the problem of robust state feedback control of networked control systems with a simple congestion control scheme. This simple congestion control scheme is based on comparing current measurements with last transmitted measurements. If their difference is less than a prescribed percentage of the current measurements then no measurement is transmitted to the controller. The controller always uses the last transmitted measurements to control the system. With this simple congestion control scheme, a robust \(\mathcal {H}_{\infty}\) state feedback controller design methodology is developed based on the Lyapunov–Krasovskii functional approach. Sufficient conditions for the existence of delay mode dependent controllers are given in terms of bilinear matrix inequalities (BMIs). These BMIs are converted into quasi-convex linear matrix inequalities (LMIs) and solved by using the cone complementarity linearization algorithm. The effectiveness of the simple congestion control in terms of reducing the network bandwidth is elaborated using simulation examples.

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References

  1. A. Bemporad, M. Heemels, M. Johansson, in Networked Control Systems. Lecture Notes in Control and Information Sciences (2010)

    Chapter  Google Scholar 

  2. E.K. Boukas, Z.K. Liu, Robust stability and stabilizability of Markov jump linear uncertain systems with mode-dependent time delays. J. Optim. Theory Appl. 109(3), 587–600 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. E.K. Boukas, P. Shi, M. Karan, C.Y. Kaya, Linear discrete-time systems with Markovian jumps and mode dependent time-delay: stability and stabilizability. Math. Probl. Eng. 8(2), 123–133 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. S. Chae, F. Rasool, S.K. Nguang, A. Swain, Robust mode delay-dependent \(\mathcal {H}_{\infty}\) control of discrete-time systems with random communication delays. IET Control Theory Appl. 04(6), 936–944 (2009)

    Article  MathSciNet  Google Scholar 

  5. W.H. Chen, W.X. Zheng, Robust stabilization of delayed Markovian jump systems subject to parametric uncertainties, in Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, USA (2007), pp. 3054–3059

    Google Scholar 

  6. M.B.G. Cloosterman, L. Hetel, N. van de Wouwa, W.P.M.H. Heemels, J. Daafouz, H. Nijmeijer, Controller synthesis for networked control systems. Automatica 46, 1584–1594 (2010)

    Article  MATH  Google Scholar 

  7. D. Delchamps, Stabilizing a linear system with quantized state feedback. IEEE Trans. Autom. Control 35, 916–924 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  8. N. Elia, S.K. Mitter, Stabilization of linear systems with limited information. IEEE Trans. Autom. Control 46, 1384–1400 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. E. Fridman, A. Seuret, J.P. Richard, Robust sampled-data stabilization of linear systems: an input delay approach. Automatica 40, 1441–1446 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. H. Fujioka, Stability analysis for a class of networked/embedded control systems: output feedback case, in Proceedings of the 17th IFAC World Congress, Seoul, Korea (2008), pp. 4210–4215

    Google Scholar 

  11. H. Gao, T. Chen, J. Lam, A new delay system approach to network-based control, in Automatica, vol. 44 (2008), pp. 39–52

    Google Scholar 

  12. L. Ghaoui, F. Oustry, M. AitRami, A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Trans. Autom. Control 42(8), 1171–1176 (1997)

    Article  MATH  Google Scholar 

  13. H. Hamidian, A. Jalali, Calculation of PID controller parameters for unstable first order time delay systems. Int. J. Sci. Eng. Res. 3(3) (2011)

  14. W.P.M.H. Heemels, A.R. Teel, N. van de Wouw, D. Nesic, Networked control systems with communication constraints: trade offs between transmission intervals, delays and performance. IEEE Trans. Autom. Control 55, 1781–1796 (2010)

    Article  Google Scholar 

  15. W.-H. Ho, S.-H. Chen, I.-T. Chen, J.-H. Chou, C.-C. Sho, Design of stable and quadratic-optimal static output feedback controller for TS-fuzzy model based control system: an integrative computational approach, in International Journal of Innovative Computing, Information and Control, vol. 8 (2012), pp. 403–418

    Google Scholar 

  16. D. Huang, S.K. Nguang, State feedback control of uncertain networked control systems with random time delays. IEEE Trans. Autom. Control 53(3), 829–834 (2008)

    Article  MathSciNet  Google Scholar 

  17. Y. Ishidoa, K. Takabaa, D.E. Quevedob, Stability analysis of networked control systems subject to packet-dropouts and finite-level quantization. Syst. Control Lett. 60(5), 325–332 (2011)

    Article  Google Scholar 

  18. K. Ji, W.j. Kim, Real-time control of networked control systems via ethernet. Int. J. Control. Autom. Syst. 3, 591–599 (2005)

    Google Scholar 

  19. R. Kalman, Nonlinear aspects of sampled data control systems, in Proceedings of the Symposium on Nonlinear Circuit Theory, Brooklyn, NY (1956)

    Google Scholar 

  20. E. Konaka, Stability of networked control system with dynamic quantizer and data-driven zero-order hold, in Electronics and Communications in Japan, vol. 94 (2011), pp. 46–52

    Google Scholar 

  21. L. Mirkin, Some remarks on the use of time-varying delay to model sample and hold circuits. IEEE Trans. Autom. Control 52(6), 1109–1112 (2007)

    Article  MathSciNet  Google Scholar 

  22. N.J. Ploplys, P.A. Kawka, A. Alleyne, Closed-loop control over wireless networks. IEEE Control Syst. Mag. 24, 58–71 (2004)

    Article  Google Scholar 

  23. T.N. Quang, I. Holic, V. Vesel, Robust guaranteed cost controller design for networked control systems: discretized approach. Int. J. Innov. Comput. Inf. Control 7(6), 3533–3544 (2011)

    Google Scholar 

  24. F. Rasool, S.K. Nguang, Quantized robust control of discrete-time systems with random communication delays. Int. J. Syst. Sci. 129–138 (2011)

  25. F. Rasool, D. Huang, S.K. Nguang, Robust \(\mathcal {H}_{\infty}\) output feedback control of networked control systems with multiple quantizers. J. Franklin Inst. 349(3), 1153–1173 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  26. F. Rasool, S.K. Nguang, M. Krug, Robust \(\mathcal {H}_{\infty}\)output feedback control of discrete-time networked systems with adaptive quantizers, in 6th IEEE Conference on Industrial Electronics and Applications, China (2011), pp. 1535–1540

    Google Scholar 

  27. Y. Shi, B. Yu, Robust mixed \(\mathcal{H}_{2}/\) \(\mathcal {H}_{\infty}\) control of networked control systems with random time delays in both forward and backward communication links. Automatica 47(4), 754–760 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  28. X. Su, P. Shi, L. Wu, Y.-D. Song, A novel control design on discrete-time Takagi–Sugeno fuzzy systems with time-varying delays. IEEE Trans. Fuzzy Syst. (2012). doi:10.1109/TFUZZ.2012.2226941

    Google Scholar 

  29. X. Su, P. Shi, L. Wu, Y.-D. Song, A novel approach to filter design for T-S fuzzy discrete-time systems with time-varying delayin. IEEE Trans. Fuzzy Syst. 20(06), 1114–1129 (2012)

    Article  Google Scholar 

  30. Y. Wang, G. Yang, Multiple communication channels-based packet dropout compensation for networked control systems. IET Control Theory Appl. 2, 717–727 (2008)

    Article  MathSciNet  Google Scholar 

  31. J. Wu, T. Chen, Design of networked control systems with packet dropouts. IEEE Trans. Autom. Control 52(7), 1314–1319 (2007)

    Article  Google Scholar 

  32. R. Yang, P. Shi, G.-P. Liu, Filtering for discrete-time networked nonlinear systems with mixed random delays and packet dropouts. IEEE Trans. Autom. Control 11(56), 2655–2660 (2011)

    Article  MathSciNet  Google Scholar 

  33. R. Yang, P. Shi, G.-P. Liu, H. Gao, Network-based feedback control for systems with mixed delays based on quantization and dropout compensation. Automatica 47(12), 2805–2809 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  34. W.-A. Zhang, L. Yu, S. Yin, A switched system approach to \(\mathcal {H}_{\infty}\) control of networked control systems with time-varying delays. J. Franklin Inst. 348(4), 165–178 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  35. Y.-B. Zhao, Y. Kang, G.-P. Liu, D. Rees, Stochastic stabilization of packet-based networked control systems. Int. J. Innov. Comput. Inf. Control 7(5A), 2441–2456 (2011)

    Google Scholar 

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Authors and Affiliations

  1. The Department of Electrical and Computer Engineering, The University of Auckland, 92019, Auckland, New Zealand

    Faiz Rasool & Sing Kiong Nguang

  2. Department o Electrical Engineering, Yuan Ze University, 135, Far-East Rd, Chung-Li, Tao-Yuan, 320, Taiwan

    Chih-Min Lin

Authors
  1. Faiz Rasool
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  2. Sing Kiong Nguang
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  3. Chih-Min Lin
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Correspondence to Faiz Rasool.

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Rasool, F., Nguang, S.K. & Lin, CM. Robust \(\mathcal{H}_{\infty}\) State Feedback Control of Networked Control Systems with Congestion Control. Circuits Syst Signal Process 32, 2761–2781 (2013). https://doi.org/10.1007/s00034-013-9591-6

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  • DOI: https://doi.org/10.1007/s00034-013-9591-6

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