access icon free Sampled-data control of fuzzy systems based on the intelligent digital redesign method via an improved fuzzy Lyapunov functional approach

© The Institution of Engineering and Technology
Received 06/04/2017, Accepted 26/09/2017, Revised 21/08/2017, Published 27/09/2017

This study presents a linear matrix inequality (LMI) approach to the sampled-data control of Takagi–Sugeno fuzzy systems, based on the intelligent digital redesign (IDR) technique. The objective of the IDR is to design a digital control system whose trajectory closely matches that of a given well-constructed analogue control system by minimising the state-matching error. In this study, state-matching performance is enhanced by using a continuous-time state-matching criterion, which guarantees that the state-matching error is minimised through the entire time interval. Unlike previous studies, mismatched information of membership functions for both analogue and digital control systems is directly manipulated. Moreover, the authors introduce an improved fuzzy Lyapunov functional that consists of both membership functions for analogue and digital control systems, which relaxes the conservativeness of LMI conditions. Finally, two examples demonstrating the effectiveness of the authors' method are provided.

Inspec keywords: digital control; minimisation; linear matrix inequalities; fuzzy control; Lyapunov methods; sampled data systems; control system synthesis; continuous time systems; fuzzy systems

Other keywords: state-matching performance; membership functions; analogue control system; LMI approach; continuous-time state-matching criterion; digital control system; intelligent digital redesign method; state-matching error minimization; linear matrix inequality; improved fuzzy Lyapunov functional approach; Takagi-Sugeno fuzzy systems; IDR technique; sampled-data control

Subjects: Fuzzy control; Optimisation techniques; Algebra; Control system analysis and synthesis methods; Stability in control theory; Discrete control systems

References

    1. 1)
      • 15. Wu, Z.G., Shi, P., Su, H., et al: ‘Sampled-data fuzzy control of chaotic systems based on a T-S fuzzy model’, IEEE Trans. Fuzzy Syst., 2014, 22, (1), pp. 153–163.
    2. 2)
      • 1. Lee, H.J., Kim, H., Joo, Y.H., et al: ‘A new intelligent digital redesign for T–S fuzzy systems: global approach’, IEEE Trans. Fuzzy Syst., 2004, 12, (2), pp. 274–284.
    3. 3)
      • 3. Sung, H.C., Kim, D.W., Park, J.B., et al: ‘Robust digital control of fuzzy systems with parametric uncertainties: LMI-based digital redesign approach’, Fuzzy Sets Syst., 2010, 161, pp. 919–933.
    4. 4)
      • 22. Oliveira, J.V., Bernussou, J., Geromel, J.C.: ‘A new discrete-time robust stability condition’, Syst. Control Lett., 1999, 37, (4), pp. 261–265.
    5. 5)
      • 18. Tanaka, K., Wang, H.O.: ‘Fuzzy control systems design and analysis: a linear matrix inequality approach’ (John Wiley and Sons, 2004).
    6. 6)
      • 21. Gu, K.: ‘An integral inequality in the stability problem of time-delay systems’. 39th IEEE Conference on Decision and Control, 2000, pp. 2805–2810.
    7. 7)
      • 2. Lee, H.J., Park, J.B., Joo, Y.H.: ‘Further refinement on LMI-based digital redesign: delta-operator approach’, IEEE Trans. Circuits Syst. II, Express Briefs, 2006, 53, (6), pp. 473–477.
    8. 8)
      • 26. Sturm, J.F.: ‘Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones’, Optim. Math. Softw., 1999, 11, pp. 625–653.
    9. 9)
      • 12. Yang, F., Zhang, H.: ‘T–S model-based relaxed reliable stabilization of networked control systems with time-varying delays under variable sampling’, Int. J. Fuzzy Syst., 2011, 13, (4), pp. 260–269.
    10. 10)
      • 7. Yoneyama, J.: ‘Robust sampled-data stabilization of uncertain fuzzy systems via input delay approach’, Afr. J. Libr. Arch. Inf. Sci., 2012, 198, pp. 169–176.
    11. 11)
      • 27. Kim, H.S., Park, J.B., Joo, Y.H.: ‘A systematic approach to fuzzy-model-based robust H-infinity control design for a quadrotor UAV under imperfect premise matching’, Int. J. Fuzzy Syst., 2017, 19, (4), pp. 1227–1237.
    12. 12)
      • 13. Sakthivel, R., Selvi, S., Mathiyalagan, K., et al: ‘Reliable mixed H-infinity and passivity-based control for fuzzy markovian switching systems with probabilistic time delays and actuator failures’, IEEE Trans. Cybern., 2015, 45, (12), pp. 2720–2731.
    13. 13)
      • 24. Bouabdallah, S., Noth, A., Siegwart, R.: ‘PID vs LQ control techniques applied to an indoor micro quadrotor’. IEEE/RSJ Int. Conf. Intteligent Robots and Systems, 2004, pp. 2451–2456.
    14. 14)
      • 8. Yang, F., Zhang, H., Hui, G., et al: ‘Mode-independent fuzzy fault-tolerant variable sampling stabilization of nonlinear networked systems with both time-varying and random delays’, Fuzzy Sets Syst., 2012, 207, pp. 45–63.
    15. 15)
      • 9. Yang, F., Zhang, H., Wang, Y.: ‘An enhanced input-delay approach to sampled-data stabilization of T–S fuzzy systems via mixed convex combination’, Nonlinear Dyn., 2014, 75, (3), pp. 501–512.
    16. 16)
      • 16. Wang, Z.P., Wu, H.N.: ‘On fuzzy sampled-data control of chaotic systems via a time-dependent Lyapunov functional approach’, IEEE Trans. Cybern., 2015, 45, (4), pp. 819–829.
    17. 17)
      • 5. Koo, G.B., Park, J.B., Joo, Y.H.: ‘Intelligent digital redesign for non-linear systems: observer-based sampled-data fuzzy control approach’, IET Control Theory Appl., 2016, 10, (1), pp. 1–9.
    18. 18)
      • 6. Lam, H.K., Ling, W.K.: ‘Sampled-data fuzzy controller for continuous nonlinear systems’, IEEE Trans. Syst. Man Cybern., 2008, 2, (1), pp. 32–39.
    19. 19)
      • 17. Lam, H.K.: ‘Stabilization of nonlinear systems using sampled-data output-feedback fuzzy controller based on polynomial-fuzzy-model-based control approach’, IEEE Trans. Syst. Man Cybern., 2012, 42, (1), pp. 258–267.
    20. 20)
      • 10. Zhu, X.L., Chen, B., Yue, D., et al: ‘An improved input delay approach to stabilization of fuzzy systems under variable sampling’, IEEE Trans. Fuzzy Syst., 2012, 20, (2), pp. 330–341.
    21. 21)
      • 23. Lee, H.J., Park, J.B., Chen, G.: ‘Robust fuzzy control of nonlinear systems with parametric uncertainties’, IEEE Trans. Fuzzy Syst., 2001, 9, (2), pp. 369–379.
    22. 22)
      • 14. Selvaraj, P., Kaviarasan, B., Sakthivel, R., et al: ‘Fault-tolerant SMC for Takagi–Sugeno fuzzy systems with time-varying delay and actuator saturation’, IET Control Theory Appl., 2017, 11, (8), pp. 1112–1123.
    23. 23)
      • 25. Löfberg, J.: ‘YALMIP: a toolbox for modeling and optimization in MATLAB’. CACSD Conf., 2004, pp. 284–289.
    24. 24)
      • 19. Tanaka, K., Hori, T., Wang, H.O.: ‘A multiple Lyapunov function approach to stabilization of fuzzy control systems’, IEEE Trans. Fuzzy Syst., 2003, 11, (4), pp. 582–589.
    25. 25)
      • 11. Sakthivel, R., Kaviarasan, B., Ma, Y.K., et al: ‘Sampled-data reliable stabilization of T–S fuzzy systems and its application’, Complexity, 2016, 21, (2), pp. 518–529.
    26. 26)
      • 4. Koo, G.B., Park, J.B., Joo, Y.H.: ‘Intelligent digital redesign for nonlinear systems using a guaranteed cost control method’, Int. J. Control Autom. Syst., 2013, 11, (6), pp. 1075–1083.
    27. 27)
      • 20. Kim, H.S., Park, J.B., Joo, Y.H.: ‘Relaxed stability conditions for the Takagi–Sugeno fuzzy system using a polynomial non-quadratic Lyapunov function’, IET Control Theory Appl., 2016, 10, (13), pp. 1590–1599.
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