http://iet.metastore.ingenta.com
1887

Membership-Function-Dependent Stability Analysis of Interval Type-2 Polynomial Fuzzy-Model-Base Control Systems

Membership-Function-Dependent Stability Analysis of Interval Type-2 Polynomial Fuzzy-Model-Base Control Systems

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

In this paper, the stability analysis for interval type-2 (IT2) polynomial fuzzy-model-based (PFMB) control system using the information of membership functions is investigated. To tackle uncertainties, IT2 membership functions are used in the IT2 polynomial fuzzy model and IT2 polynomial fuzzy controller. The stability of IT2 PFMB control system is investigated based on the Lyapunov stability theory and both sets of membership function independent (MFI) and membership function dependent (MFD) stability conditions are derived on the basis of the sum-of-squares (SOS) approach. To make the stability conditions MFD, the boundary information of IT2 membership functions is used in the stability analysis. To extract richer information of IT2 membership functions, the operating domain is partitioned into sub-domains. In each sub-domain, the boundary information of IT2 membership functions and those of the upper and lower membership function are obtained. Furthermore, to further relax the conservativeness, a switching polynomial fuzzy controller, together with the informations obtained in each sub-domain, is employed in investigating the stability analysis. Numerical examples and simulation results are given to demonstrate the validity of MFD and MFD switching methods.

References

    1. 1)
      • 1. Takagi, T., Sugeno, M.: ‘Fuzzy identification of systems and its applications to modeling and control’, IEEE Trans. Syst. Man. Cybern., 1985, SMC-15, (1), pp. 116132.
    2. 2)
      • 2. Sugeno, M., Kang, G.: ‘Structure identification of fuzzy model’, Fuzzy Sets Syst., 1988, 28, (1), pp. 1533.
    3. 3)
      • 3. Lam, H.K., Narimani, M.: ‘Stability analysis of polynomial-fuzzy-model-based control systems using switching polynomial Lyapunov function’, IEEE Trans. Fuzzy Syst., 2013, 21, (5), pp. 800813.
    4. 4)
      • 4. Lam, H.K., Leung, F.: ‘Stability analysis of fuzzy control systems subject to uncertain grades of membership’, IEEE Trans. Syst. Man. Cybern B, Cybern., 2005, 35, (6), pp. 13221325.
    5. 5)
      • 5. Lam, H.K., Narimani, M.: ‘Stability analysis and performance design for fuzzy-model-based control system under imperfect premise matching’, IEEE Trans. Fuzzy Syst., 2009, 17, (4), pp. 949961.
    6. 6)
      • 6. Sala, A., Arino, C.: ‘Relaxed stability and performance conditions for Takagi–Sugeno fuzzy systems with knowledge on membership function overlap’, IEEE Trans. Syst. Man. Cybern B, Cybern., 2007, 37, (3), pp. 727732.
    7. 7)
      • 7. Sala, A., Ariño, C.: ‘Relaxed stability and performance LMI conditions for Takagi–Sugeno fuzzy systems with polynomial constraints on membership function shapes’, IEEE Trans. Fuzzy Syst., 2008, 16, (5), pp. 13281336.
    8. 8)
      • 8. Tseng, C., Chen, B., Uang, H.: ‘Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model’, IEEE Trans. Fuzzy Syst., 2001, 9, (3), pp. 381392.
    9. 9)
      • 9. Lin, C., Wang, Q., Lee, T.: ‘H output tracking control for nonlinear systems via T--S fuzzy model approach’, IEEE Trans. Syst. Man. Cybern B, Cybern, 2006, 36, (2), pp. 450457.
    10. 10)
      • 10. Lam, H.K., Seneviratne, L.: ‘Tracking control of sampled-data fuzzy-model-based control systems’, IET Control Theory Appl., 2009, 3, (1), pp. 5667.
    11. 11)
      • 11. Cao, Y., Frank, P.: ‘Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models’, Fuzzy Sets Syst., 2001, 124, (2), pp. 213229.
    12. 12)
      • 12. Cao, Y., Frank, P.: ‘Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach’, IEEE Trans. Fuzzy Syst., 2000, 8, (2), pp. 200211.
    13. 13)
      • 13. Lian, K., Chiu, C., Chiang, T., et al.: ‘LMI-based fuzzy chaotic synchronization and communications’, IEEE Trans. Fuzzy Syst., 2001, 9, (4), pp. 539553.
    14. 14)
      • 14. Wang, Y., Guan, Z., Wang, H.: ‘LMI-based fuzzy stability and synchronization of Chen's system’, Phys. Lett. A, 2003, 320, (2-3), pp. 154159.
    15. 15)
      • 15. Tanaka, K., Yoshida, H., Ohtake, H., et al.: ‘A sum-of-squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems’, IEEE Trans. Fuzzy Syst., 2009, 17, (4), pp. 911922.
    16. 16)
      • 16. Tanaka, K., Yoshida, H., Ohtake, H., et al.: ‘Stabilization of polynomial fuzzy systems via a sum of squares approach’. Proc. 2007 IEEE 22nd Int. Symp. Intelligent Control, 2007, pp. 160165.
    17. 17)
      • 17. Narimani, M., Lam, H.K.: ‘SOS-based stability analysis of polynomial fuzzy-model-based control systems via polynomial membership functions’, IEEE Trans. Fuzzy Syst., 2010, 18, (5), pp. 862871.
    18. 18)
      • 18. Lam, H.K.: ‘Polynomial fuzzy-model-based control systems: stability analysis via piecewise-linear membership functions’, IEEE Trans. Fuzzy Syst., 2011, 19, (3), pp. 588593.
    19. 19)
      • 19. Xiao, B., Lam, H.K., Li, H.: ‘Stabilization of interval type-2 polynomial-fuzzy-model-based control systems’, IEEE Trans. Fuzzy Syst., 2017, 25, (1), pp. 205217.
    20. 20)
      • 20. Papachristodoulou, A., Prajna, S.: ‘A tutorial on sum of squares techniques for systems analysis’. Proc. 2005, American Control Conf., 2005, vol. 4, 2005, pp. 26862700.
    21. 21)
      • 21. Tanaka, K., Yoshida, H., Ohtake, H., et al.: ‘A sum of squares approach to stability analysis of polynomial fuzzy systems’. Proc. 2007 American Control Conf., 2007, pp. 40714076.
    22. 22)
      • 22. Prajna, S., Papachristodoulou, A., Parrilo, P.: ‘Sum of squares optimization toolbox for MATLAB user's guide’, 2004.
    23. 23)
      • 23. Lam, H.K., Tsai, S.: ‘Stability analysis of polynomial-fuzzy-model-based control systems with mismatched premise membership functions’, IEEE Trans. Fuzzy Syst., 2014, 22, (1), pp. 223229.
    24. 24)
      • 24. Liang, Q., Mendel, J.: ‘Interval type-2 fuzzy logic systems: theory and design’, IEEE Trans. Fuzzy Syst., 2000, 8, (5), pp. 535550.
    25. 25)
      • 25. Mendel, J., John, R., Liu, F.: ‘Interval type-2 fuzzy logic systems made simple’, IEEE Trans. Fuzzy Syst., 2006, 14, (6), pp. 808821.
    26. 26)
      • 26. Karnik, N., Mendel, J.: ‘Introduction to type-2 fuzzy logic systems’. Proc. 1998 IEEE Int. Conf. Fuzzy Systems Proc. IEEE World Congress on Computational Intelligence (Cat. No. 98CH36228), vol. 2, 1998, pp. 915920.
    27. 27)
      • 27. Karnik, N.N., Mendel, J.M., Liang, Q.: ‘Type-2 fuzzy logic systems’, IEEE Trans. Fuzzy Syst., 1999, 7, (6), pp. 643658.
    28. 28)
      • 28. Lam, H.K., Seneviratne, L.: ‘Stability analysis of interval type-2 fuzzy-model-based control systems’, IEEE Trans. Syst. Man Cybern. B, Cybern., 2008, 38, (3), pp. 617628.
    29. 29)
      • 29. Lam, H.K., Li, H., Deters, C., et al.: ‘Control design for interval type-2 fuzzy systems under imperfect premise matching’, IEEE Trans. Ind. Electron, 2014, 61, (2), pp. 956968.
    30. 30)
      • 30. Li, H., Wu, C., Shi, P., et al.: ‘Control of nonlinear networked systems with packet dropouts: Interval type-2 fuzzy model-based approach’, IEEE Trans. Cybern., 2015, 45, (11), pp. 23782389.
    31. 31)
      • 31. Li, H., Sun, X., Wu, L., et al.: ‘State and output feedback control of interval type-2 fuzzy systems with mismatched membership functions’, IEEE Trans. Fuzzy Syst., 2015, 23, (6), pp. 19431957.
    32. 32)
      • 32. Li, H., Pan, Y., Zhou, Q.: ‘Filter design for interval type-2 fuzzy systems with d stability constraints under a unified frame’, IEEE Trans. Fuzzy Syst., 2015, 23, (3), pp. 719725.
    33. 33)
      • 33. Li, H., Wu, C., Wu, L., et al.: ‘Filtering of interval type-2 fuzzy systems with intermittent measurements’, IEEE Trans. Cybern., 2016, 46, (3), pp. 668678.
    34. 34)
      • 34. Zhao, T., Dian, S.: ‘State feedback control for interval type-2 fuzzy systems with time-varying delay and unreliable communication links’, IEEE Trans. Fuzzy Syst., 2017, PP, (99), pp. 11.
    35. 35)
      • 35. Liu, J., Wu, C., Wang, Z., et al.: ‘Reliable filter design for sensor networks in the type-2 fuzzy framework’, IEEE Trans. Ind. Inf., 2017, PP, (99), pp. 11.
    36. 36)
      • 36. Zhao, T., Dian, S.: ‘Delay-dependent stabilization of discrete-time interval type-2 T-S fuzzy systems with time-varying delay’, J. Franklin Inst., 2017, 354, (3), pp. 15421567.
    37. 37)
      • 37. Xiao, B., Lam, H.K., Song, G., et al.: ‘Output-feedback tracking control for interval type-2 polynomial fuzzy-model-based control systems’, Neurocomputing, 2017, 242, pp. 8395.
    38. 38)
      • 38. Lam, H.K., Seneviratne, L.: ‘Stability analysis of polynomial fuzzy-model-based control systems under perfect/imperfect premise matching’, IET Control Theory Appl., 2011, 5, (15), pp. 16891697.
    39. 39)
      • 39. Lam, H.K., Liu, C., Wu, L., et al.: ‘Polynomial fuzzy-model-based control systems: Stability analysis via approximated membership functions considering sector nonlinearity of control input’, IEEE Trans. Fuzzy Syst., 2015, 23, (6), pp. 22022214.
    40. 40)
      • 40. Zhao, Y., Xiao, B., Liu, C., et al.: ‘Relaxed LMI-based stability conditions for fuzzy-model-based control systems under imperfect premise matching: approximated membership function approach’. Proc. 11th World Congress on Intelligent Control and Automation, 2014, pp. 251256.
    41. 41)
      • 41. Sala, A., Arino, C.: ‘Polynomial fuzzy models for nonlinear control: a taylor series approach’, IEEE Trans. Fuzzy Syst., 2009, 17, (6), pp. 12841295.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2017.0288
Loading

Related content

content/journals/10.1049/iet-cta.2017.0288
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address