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H ∞ Control of Piecewise-Linear Systems Under Unreliable Communication Links

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Abstract

This paper considers the problem of H ∞ control of piecewise-linear control systems under unreliable communication links. Due to the limited bandwidth of the channels, signal transmission delays and data packet losses can occur between the plant and the controller. In the presence of random signal transmission delays and data packet losses, a piecewise controller is designed to stabilize the piecewise-linear system in the sense of mean square and also achieve a prescribed H ∞ disturbance attenuation performance based on piecewise-quadratic Lyapunov–Krasovskii functionals. It is shown that the H ∞ controllers can be designed by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. Moreover, the controller design method is further extended to uncertain case where the system matrices’ uncertainties are represented in polytopic frameworks. Finally, an example is provided to illustrate the effectiveness of the developed theoretical results.

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References

  1. P.J. Antsaklis, J. Baillieul, Guest editorial: Special issue on networked control systems. IEEE Trans. Autom. Control 49, 1421–1597 (2004)

    Article  MathSciNet  Google Scholar 

  2. S. Azuma, E. Yanagisawa, J. Imura, Controllability analysis of biosystems based on piecewise-affine systems approach. IEEE Trans. Autom. Control 53, 139–152 (2008)

    Article  MathSciNet  Google Scholar 

  3. S.P. Banks, S.A. Khathur, Structure and control of piecewise-linear systems. Int. J. Control 50, 667–686 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  4. L.O. Chua, The double scroll. IEEE Trans. Circuits Syst. I 32, 797–817 (1985)

    MathSciNet  MATH  Google Scholar 

  5. L.O. Chua, A. Deng, Canonical piecewise-linear modeling. IEEE Trans. Circuits Syst. 33, 511–525 (1986)

    Article  Google Scholar 

  6. L.O. Chua, R. Ying, Canonical piecewise-linear analysis. IEEE Trans. Circuits Syst. 30, 125–140 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  7. F.A. Cuzzola, M. Morari, An LMI approach for H ∞ analysis and control of discrete-time piecewise affine systems. Int. J. Control 75, 1293–1301 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. H.L. Dong, Z.D. Wang, W.C. Ho Daniel, H.J. Gao, Robust H ∞ fuzzy output-feedback control with multiple probabilistic delays and multiple missing measurements. IEEE Trans. Fuzzy Syst. 18, 712–725 (2010)

    Article  Google Scholar 

  9. H.L. Dong, Z.D. Wang, W.C. Ho Daniel, H.J. Gao, Variance-constrained H ∞ filtering for nonlinear time-varying stochastic systems with multiple missing measurements: the finite-horizon case. IEEE Trans. Signal Process. 58, 2534–2543 (2010)

    Article  MathSciNet  Google Scholar 

  10. H.L. Dong, Z.D. Wang, H.J. Gao, Robust H ∞ filtering for a class of nonlinear networked systems with multiple stochastic communication delays and packet dropouts. IEEE Trans. Signal Process. 58, 1957–1966 (2010)

    Article  MathSciNet  Google Scholar 

  11. 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 

  12. G. Feng, Stability analysis of piecewise discrete-time linear systems. IEEE Trans. Autom. Control 47, 1108–1112 (2002)

    Article  Google Scholar 

  13. G. Feng, Controller design and analysis of uncertain piecewise-linear systems. IEEE Trans. Circuits Syst. I 49, 224–232 (2002)

    Article  Google Scholar 

  14. H.J. Gao, T.W. Chen, H ∞ estimation for uncertain systems with limited communication capacity. IEEE Trans. Autom. Control 52, 2070–2084 (2008)

    Article  MathSciNet  Google Scholar 

  15. H.J. Gao, T.W. Chen, Network-based H ∞ output tracking control. IEEE Trans. Autom. Control 53, 655–667 (2008)

    Article  MathSciNet  Google Scholar 

  16. H.J. Gao, T.W. Chen, T.Y. Chai, Passivity and passification for networked control systems. SIAM J. Control Optim. 46, 1299–1322 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  18. H.J. Gao, X.B. Yang, P. Shi, Multi-objective robust H ∞ control of spacecraft rendezvous. IEEE Trans. Control Syst. Technol. 17, 794–802 (2009)

    Article  Google Scholar 

  19. H.J. Gao, Y. Zhao, T. W Chen, H ∞ fuzzy control of nonlinear systems under unreliable communication links. IEEE Trans. Fuzzy Syst. 17, 265–287 (2009)

    Article  Google Scholar 

  20. G.C. Goodwin, H. Haimovich, D.E. Quevedo, J.S. Welsh, A moving horizon approach to networked control system design. IEEE Trans. Autom. Control 49, 1427–1445 (2004)

    Article  MathSciNet  Google Scholar 

  21. P. Grieder, M. Kvasnica, M. Baoti, M. Morari, Stabilizing low complexity feedback control of constrained piecewise affine systems. Automatica 41, 1683–1694 (2005)

    Article  MATH  Google Scholar 

  22. S.W. Hu, W.Y. Yan, Stability robustness of networked control systems with respect to packet loss. Automatica 43, 1243–1248 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  23. J.I. Imura, A. van der Schaft, Characterization of well-posedness of piecewise-linear systems. IEEE Trans. Autom. Control 45, 1600–1619 (2000)

    Article  MATH  Google Scholar 

  24. H. Ishii, H ∞ control with limited communication and message losses. Syst. Control Lett. 57, 322–331 (2008)

    Article  MATH  Google Scholar 

  25. W. Jing, T.W. Chen, Design of networked control systems with packet dropouts. IEEE Trans. Autom. Control 52, 1314–1319 (2007)

    Article  Google Scholar 

  26. M. Johansson, A. Rantzer, Computation of piecewise quadratic Lyapunov functions for hybrid systems. IEEE Trans. Autom. Control 43, 555–559 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  27. X.Y. Meng, J. Lam, B.Z. Du, H.J. Gao, A delay-partitioning approach to the stability analysis of discrete-time systems. Automatica 46, 610–614 (2010)

    Article  MATH  Google Scholar 

  28. L.A. Montestruque, P. Antsaklis, Stability of model-based networked control systems with time-varying transmission times. IEEE Trans. Autom. Control 49, 1562–1572 (2004)

    Article  MathSciNet  Google Scholar 

  29. Y.S. Moon, P. Park, W.H. Kwon, Y.S. Lee, Delay-dependent robust stabilization of uncertain state-delayed systems. Int. J. Control 74, 1447–1455 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  30. I.R. Petersen, A stabilization algorithm for a class of uncertain linear systems. Syst. Control Lett. 8, 351–357 (1987)

    Article  MATH  Google Scholar 

  31. A. Rantzer, M. Johansson, Piecewise linear quadratic optimal control. IEEE Trans. Autom. Control 45, 629–637 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  32. L. Rodrigues, E.K. Boukas, Piecewise-linear H ∞ controller synthesis with applications to inventory control of switched production systems. Automatica 42, 1245–1254 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  33. L. Rodrigues, S. Boyd, Piecewise-affine state feedback for piecewise-affine slab systems using convex optimization. Syst. Control Lett. 54, 835–853 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  34. P. Seiler, R. Sengupta, An H ∞ approach to networked control. IEEE Trans. Autom. Control 50, 356–364 (2005)

    Article  MathSciNet  Google Scholar 

  35. E.D. Sontag, Nonlinear regulation: the piecewise linear approach. IEEE Trans. Autom. Control 26, 346–357 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  36. P.Y. Tiwari, E.F. Mulder, M.V. Kothare, Synthesis of stabilizing antiwindup controllers using piecewise quadratic Lyapunov functions. IEEE Trans. Autom. Control 52, 2341–2345 (2007)

    Article  MathSciNet  Google Scholar 

  37. G.C. Walsh, H. Ye, L. Bushnell, Stability analysis of networked control systems. IEEE Trans. Control Syst. Technol. 10, 438–446 (2002)

    Article  Google Scholar 

  38. Z.D. Wang, F.W. Yang, D.W.C. Ho, X.H. Liu, Robust H ∞ filtering for stochastic time-delay systems with missing measurements. IEEE Trans. Signal Process. 54, 2579–2587 (2006)

    Article  Google Scholar 

  39. Z.D. Wang, F.W. Yang, D.W.C. Hom, X.H. Liu, Robust H ∞ Control for networked systems with random packet losses. IEEE Trans. Syst. Man Cybern., Part B 37, 816–924 (2007)

    Google Scholar 

  40. H. Xiao, Z.D. Wang, D. Zhou, Robust H ∞ filtering for networked systems with multiple state delays. Int. J. Control 80, 1217–1232 (2007)

    Article  MATH  Google Scholar 

  41. J.L. Xiong, J. Lam, Stabilization of linear systems over networks with bounded packet loss. Automatica 43, 80–87 (2005)

    Article  MathSciNet  Google Scholar 

  42. S.Y. Xu, J. Lam, T.W. Chen, Robust H ∞ control for uncertain discrete stochastic time-delay systems. Syst. Control Lett. 51, 203–215 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  43. X.B. Yang, H.J. Gao, P. Shi, Robust H ∞ control for a class of uncertain mechanical systems. Int. J. Control 83, 1303–1324 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  44. M. Yu, L. Wang, T. Chu, F. Hao, Stabilization of networked control systems with data packet dropout and transmission delays: continuous-time case. Eur. J. Control 11, 40–55 (2005)

    Article  MathSciNet  Google Scholar 

  45. D. Yue, Q.L. Han, C. Peng, State feedback controller design of networked control systems. IEEE Trans. Circuits Syst. II, Express Briefs 51, 640–644 (2004)

    Article  Google Scholar 

  46. D. Yue, Q.L. Han, J. Lam, Network-based robust H ∞ control of systems with uncertainty. Automatica 41, 999–1007 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  47. H.B. Zhang, Y.B. Yu, J. Zhang, Robust H ∞ control of piecewise-linear chaotic systems with random data loss. Chin. Phys. B 19 (2010)

  48. L. Zhang, Y. Shi, T. Chen, B. Huang, A new method for stabilization of networked control systems with random delays. IEEE Trans. Autom. Control 50(8), 1177–1181 (2005)

    Article  MathSciNet  Google Scholar 

  49. W. Zhang, M.S. Branicky, S.M. Phillips, Stability of networked control systems. IEEE Control Syst. Mag. 21(1), 84–99 (2001)

    Article  Google Scholar 

  50. W.A. Zhang, L. Yu, Output feedback stabilization of networked control systems with packer dropouts. IEEE Trans. Autom. Control 52(9), 1705–1710 (2007)

    Article  MathSciNet  Google Scholar 

  51. Y. Zhao, J. Lam, H.J. Gao, Fault detection for fuzzy systems with intermittent measurement. IEEE Trans. Fuzzy Syst. 17(2), 398–410 (2009)

    Article  Google Scholar 

  52. P.V. Zhivoglyadov, R.H. Middleton, Networked control design for linear systems. Automatica 39(4), 743–750 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Centre for Nonlinear and Complex Systems, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, P.R. China

    Hongbin Zhang

  2. Department of Systems Engineering & Engineering Management, City University of Hong Kong, Kowloon, Hong Kong

    Chuangyin Dang

  3. School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Jian Zhang

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  1. Hongbin Zhang
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  2. Chuangyin Dang
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  3. Jian Zhang
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Correspondence to Hongbin Zhang.

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Zhang, H., Dang, C. & Zhang, J. H ∞ Control of Piecewise-Linear Systems Under Unreliable Communication Links. Circuits Syst Signal Process 31, 1297–1318 (2012). https://doi.org/10.1007/s00034-011-9377-7

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  • DOI: https://doi.org/10.1007/s00034-011-9377-7

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