Skip to main content
SpringerLink
Log in

Interval Type-2 Fuzzy Sampled-Data Optimal Control for Nonlinear Systems with Multiple Conditions

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

The work is aimed at exploring the problem of interval type-2 (IT2) fuzzy sampled-data optimal control. Considering that the controlled system has multiple conditions such as nonlinearities, parameter uncertainties and missing data, the IT2 fuzzy system is utilized to model such the systems. By employing free-weighting matrix method, the effective control scheme formed by the linear matrix inequalities is acquired in the stable sense of Lyapunov–Krasovskii theory. And, the proposed sufficient conditions are relaxed by making the best of the attribute and boundary information of membership functions. Furthermore, the IT2 sampled-data fuzzy controller is devised, which makes the fuzzy closed-loop system keep asymptotical stability and satisfy the optimal control performance index. Finally, the fuzzy control scheme is fully verified by the inverted pendulum system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  1. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. SMC-15(1), 116–132 (1985)

    Article  MATH  Google Scholar 

  2. Tanaka, K., Sugeno, M.: Stability analysis and design of fuzzy control systems. Fuzzy Sets Syst. 45(2), 135–156 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  3. Jing, X.-J., Lam, H.K., Shi, P.: Fuzzy Sampled-data control for uncertain vehicle suspension systems. IEEE Trans. Cybern. 44(7), 1111–1126 (2014)

    Article  Google Scholar 

  4. Su, L., Ye, D.: Mixed H-infinity and passive event-triggered reliable control for T–S fuzzy Markov jump systems. Neurocomputing 281, 96–105 (2018)

    Article  Google Scholar 

  5. Li, M., Shu, F., Liu, D.-Y., et al.: Robust H-infinity control of T–S fuzzy systems with input time-varying delays: a delay partitioning method. Appl. Math. Comput. 321, 209–222 (2018)

    MathSciNet  MATH  Google Scholar 

  6. Duan, R.-R., Li, J.-M.: Observer-based non-PDC controller design for T–S fuzzy systems with the fractionalorder alpha: 0 < α < 1. IET Control Theory A. 12(5), 661–668 (2018)

    Article  Google Scholar 

  7. Kumar, S.V., Raja, R., Anthoni, S.M., et al.: Robust finite-time non-fragile sampled-data control for T–S fuzzy flexible spacecraft model with stochastic actuator faults. Appl. Math. Comput. 321, 483–497 (2018)

    MathSciNet  MATH  Google Scholar 

  8. Kim, H.S., Park, J.B., Joo, Y.H.: Sampled-data control of fuzzy systems based on the intelligent digital redesign technique: an input-delay approach. Int. J. Control Autom. 16(1), 327–334 (2018)

    Article  Google Scholar 

  9. Kim, D.W., Lee, H.J.: Direct discrete-time design approach to robust H ∞ sampled-data observer-based output-feedback fuzzy control. Int. J. Syst. Sci. 47(1), 77–91 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  10. Wang, J.-W., Li, H.-X., Wu, H.-N.: Fuzzy guaranteed cost sampled-data control of nonlinear systems coupled with a scalar reaction-diffusion process. Fuzzy Sets Syst. 302, 121–142 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  11. Liu, Y.-J., Lee, S.-M.: Stability and sabilization of Takagi-Sugeno fuzzy systems via sampled-data and state quantized controller. IEEE Trans. Fuzzy Syst. 24(3), 635–644 (2016)

    Google Scholar 

  12. Liu, W.-H., Lim, C.-C., Shi, P., Xu, S.-Y.: Sampled-data fuzzy control for a class of nonlinear systems with missing data and disturbances. Fuzzy Sets Syst. 306, 63–86 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  13. Ali, M.S., Gunasekaran, N., Zhu, Q.-X.: State estimation of T–S fuzzy delayed neural networks with Markovian jumping parameters using sampled-data control. Fuzzy Sets Syst. 306, 87–104 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lam, H.K., Senevitatne, L.D.: Stability analysis of interval type-2 fuzzy-model-based control systems. IEEE Trans. Syst. Man Cybern. Part B Cybern. 38(3), 617–628 (2008)

    Article  Google Scholar 

  15. Lam, H.K., Li, H.-Y., Deters, C., Secco, E.L., Wurdemann, H.A., Althoefer, K.: Control design for interval type-2 fuzzy systems under imperfect premise matching. IEEE Trans. Ind. Electron. 16(2), 956–968 (2014)

    Article  Google Scholar 

  16. Zhao, T., Xiao, J.: State feedback control of interval type-2 T–S fuzzy systems via interval type-2 regional switching fuzzy controllers. Int. J. Syst. Sci. 46(5), 2756–2769 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhao, T., Xiao, J., Sheng, H., Wang, T.: H∞ control of continuous-time interval type-2 T–S fuzzy systems via dynamic output feedback controllers. Neurocomputing 165, 133–143 (2015)

    Article  Google Scholar 

  18. Li, H.-Y., Wang, J.-H., Lam, H.K., Zhou, Q., Du, H.-P.: Adaptive sliding mode control for interval type-2 fuzzy systems. IEEE Trans. Syst. Man Cybern. Syst. 46(12), 1654–1663 (2016)

    Article  Google Scholar 

  19. Che, C., Peng, J.-Y., Xiao, J., et al.: Membership-function-dependent stabilization conditions for interval type-2 fuzzy time-delay systems via static output feedback scheme. Int. J. Fuzzy Syst. 20(5), 1439–1450 (2018)

    Article  MathSciNet  Google Scholar 

  20. Xiao, B., Lam, H.K., Song, G., Li, H.-Y.: Output-feedback tracking control for interval type-2 polynomial fuzzy-model-based control systems. Neurocomputing 242, 83–95 (2017)

    Article  Google Scholar 

  21. Xiao, B., Lam, H.K., Li, H.-Y.: Stabilization of interval type-2 polynomial-fuzzy-model-based control systems. IEEE Trans. Fuzzy Syst. 25(1), 205–217 (2017)

    Article  Google Scholar 

  22. Sun, D., Liao, Q.-F., Ren, H.-L.: Type-2 fuzzy modeling and control for bilateral teleoperation system with dynamic uncertainties and time-varying delays. IEEE Trans. Ind. Electron. 65(1), 447–459 (2018)

    Article  Google Scholar 

  23. Xiao, B., Lam, H.K., Yang, X.-Z., Yu, Y., Ren, H.-L.: Tracking control design of interval type-2 polynomial-fuzzy-model-based systems with time-varying delay. Eng. Appl. Artif. Intel. 75, 76–87 (2018)

    Article  Google Scholar 

  24. Huang, J., Wu, D.-R.: Interval type-2 fuzzy logic modeling and control of a mobile two-wheeled inverted pendulum. IEEE Trans. Fuzzy Syst. 26(4), 2030–2038 (2018)

    Article  MathSciNet  Google Scholar 

  25. Zheng, W., Wang, H.-B., Hua, C.-C., Zhang, Z.-M., Wang, H.R.: Dynamic output-feedback control for nonlinear continuous-time systems based on parametric uncertain subsystem and interval type-2 fuzzy model. J. Frankl. Inst. 355, 7962–7984 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  26. Li, H.-Y., Sun, X.-J., Shi, P., Lam, H.K.: Control design of interval type-2 fuzzy systems with actuator fault: sampled-data control approach. Inform. Sci. 302, 1–13 (2015)

    Article  MATH  Google Scholar 

  27. Du, Z.-B., Yan, Z.-Z., Zhao, Z.: Interval type-2 fuzzy tracking control for nonlinear systems via sampled-data controller. Fuzzy Sets Syst. 356, 92–112 (2019)

    Article  MathSciNet  Google Scholar 

  28. Li, H.-Y., Wu, C.-W., Shi, P., Gao, Y.-B.: Control of nonlinear networked systems with packet dropouts: interval type-2 fuzzy model-based approach. IEEE Trans. Cybern. 45(11), 2378–2389 (2015)

    Article  Google Scholar 

  29. Li, H.-Y., Wu, C.-W., Jing, X.-J., Wu, L.-G.: Fuzzy tracking control for nonlinear networked systems. IEEE Trans. Cybern. 47(8), 2020–2031 (2017)

    Article  Google Scholar 

  30. Zhao, T., Dian, S.-Y.: State feedback control for interval type-2 fuzzy systems with time-varying delay and unreliable communication links. IEEE Trans. Fuzzy Syst. 26(2), 951–966 (2018)

    Article  Google Scholar 

Download references

Acknowledgements

The authors are supported by the Key Program of the National Natural Science Foundation of China (11632008), the National Natural Science Foundation of China (11872189, 61703360) and the Natural Science Foundation of Shandong Province (ZR2017MF019).

Author information

Authors and Affiliations

  1. Faculty of Science, Jiangsu University, Zhenjiang, 212013, Jiangsu, China

    Zifang Qu, Zhengdi Zhang & Miao Peng

  2. School of Mathematics and Information Science, Shandong Technology and Business University, Yantai, 264005, China

    Zifang Qu

  3. School of Computer and Control Engineering, Yantai University, Yantai, 264005, Shandong, China

    Zhenbin Du

Authors
  1. Zifang Qu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhengdi Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhenbin Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Miao Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhenbin Du.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qu, Z., Zhang, Z., Du, Z. et al. Interval Type-2 Fuzzy Sampled-Data Optimal Control for Nonlinear Systems with Multiple Conditions. Int. J. Fuzzy Syst. 21, 1480–1496 (2019). https://doi.org/10.1007/s40815-019-00640-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-019-00640-y

Keywords

Search

Navigation