Skip to main content

Advertisement

Springer Nature Link
Log in

An SOS-Based Observer Design for Discrete-Time Polynomial Fuzzy Systems

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

Abstract

This paper investigates the polynomial fuzzy observer design for discrete-time uncertain polynomial systems. Three classes of discrete-time polynomial fuzzy systems are studied via a sum of squares (SOS) approach. A polynomial fuzzy system is a more general representation of the well-known Takagi–Sugeno (T–S) fuzzy system. The conditions in the proposed approach are derived in terms of SOS, which is the extension of the LMI method. Hence, the conditions obtained in this paper are more general than the corresponding LMI approaches for T–S fuzzy systems. All the design conditions in the proposed approach can be symbolically and numerically solved via the recently developed SOSTOOLS and a semidefinite-program solver, respectively. Numerical examples are provided to demonstrate the validity and applicability of the proposed SOS-based design approach.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 15(2), 116–132 (1985)

    Article  MATH  Google Scholar 

  2. Tong, S.C., Li, H.X.: Fuzzy adaptive sliding-mode control for MIMO nonlinear systems. IEEE Trans. Fuzzy Syst. 11(3), 354–360 (2003)

    Article  Google Scholar 

  3. Zhang, H.G., Liu, D.R.: Fuzzy Modeling and Fuzzy Control. Birkhauser, Boston (2006)

    MATH  Google Scholar 

  4. Wang, Y.C., Zhang, H.G., Wang, Y.Z.: Fuzzy adaptive control of stochastic nonlinear systems with unknown virtual control gain function. Acta Autom. Sinica 32(2), 170–178 (2006)

    Google Scholar 

  5. Tong, S.C., Li, Y., Li, Y.M., Liu, Y.J.: Observer-based adaptive fuzzy backstepping control for a class of stochastic nonlinear strict-feedback systems. IEEE Trans. Syst. Man Cybern. Part B 41(6), 1693–1704 (2011)

    Article  MathSciNet  Google Scholar 

  6. Zhang, H.G., Zhang, J.L., Yang, G.H., Luo, Y.H.: Leader-based optimal coordination control for the consensus problem of multi-agent differential games via fuzzy adaptive dynamic programming (published on-line on 11th, March). IEEE Trans. Fuzzy Syst. (2014). doi:10.1109/TFUZZ.2014.2310238

    Google Scholar 

  7. Yang, F.S., Zhang, H.G.: T–S model-based relaxed reliable stabilization of networked control systems with time-varying delays under variable sampling. Int. J. Fuzzy Syst. 13(4), 260–269 (2011)

    MathSciNet  Google Scholar 

  8. Zhang, H.G., Li, M., Yang, J., Yang, D.D.: Fuzzy model-based robust networked control for a class of nonlinear systems. IEEE Trans. Syst. Man Cybern. Part A 39(2), 437–447 (2009)

    Article  Google Scholar 

  9. Tanaka, K., Wang, H.O.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Wiley, Hoboken (2001)

    Book  Google Scholar 

  10. Zhang, H.G., Yang, D.D.: Guaranteed cost networked control for T–S fuzzy systems with time delays. IEEE Trans. Syst. Man Cybern. Part C 37(2), 250–265 (2007)

    Google Scholar 

  11. Feng, G.: A survey on analysis and design of model-based fuzzy control systems. IEEE Trans. Fuzzy Syst. 14(5), 676–697 (2006)

    Article  Google Scholar 

  12. Zadeh, L.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  13. Baumann, W., Rugh, W.: Feedback control of nonlinear systems by extended linearization. IEEE Trans. Autom. Control 31(1), 40–46 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  14. Tanaka, K., Yoshida, H., Ohtake, H., Wang, H. O,: Stabilization of polynomial fuzzy systems via a sum of squares approach. In: Proceeding of the 22nd IEEE International Symposium on Intelligent Control, 160–165 (2007)

  15. Tanaka, K., Yoshida, H., Ohtake, H., Wang, H.O.: Polynomial fuzzy observer designs: A sum-of-squares approach. IEEE Trans. Syst. Man Cybern. Part B 14(5), 1330–1342 (2012)

    Article  Google Scholar 

  16. Tanaka, K., Ohtake, H., Wada, M., Wang, H. O. Chen, Y.-J.: Polynomial fuzzy observer design: a sum of squares approach, In: 48th IEEE Conference on Decision and Control, 7771–7776 (2009)

  17. Seo, T., Ohtake, H., Chen, Y.J., Tanaka, K., Wang, H.O.: A polynomial observer design for a wider class of polynomial fuzzy systems. Int. Conf. Fuzzy Syst. 2011, 1305–1311 (2011)

    Google Scholar 

  18. Tanaka, K., Ohtake, H., Seo, T., Wang, H.O.: An SOS-based observer design for polynomial fuzzy systems. Am. Control Conf. 2011, 4953–4958 (2011)

    Google Scholar 

  19. Guelton, K., Manamanni, N., Duong, C.C., Koumba-Emianiwe, D.L.: Sum-of-squares stability analysis of Takagi-Sugeno systems based on multiple polynomial lyapunov functions. Int. J. Fuzzy Syst. 15(1), 1–8 (2013)

    MathSciNet  Google Scholar 

  20. Prajna, S., Papachristodoulou, A., Seiler, P., Parrilo, P.: SOSTOOLS: Sum of Squares Optimization Toolbox for MATLAB, Version 2.00. California Institute Technology, Pasadena (2004)

    Google Scholar 

  21. Sturm, J.: Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones. Optim. Methods Softw 11(4), 625–653 (1999)

    Article  MathSciNet  Google Scholar 

  22. Tong, S.C., Li, Y.M.: Adaptive fuzzy output feedback tracking backstepping control of strict-feedback nonlinear systems with unknown dead zones. IEEE Trans. Fuzzy Syst. 20(1), 168–180 (2012)

    Article  Google Scholar 

  23. Lee, C.H., Hsueh, H.Y.: Observer-based adaptive control for a class of nonlinear non-affine systems using recurrent-type fuzzy logic systems. Int. J Fuzzy Syst. 15(1), 55–65 (2013)

    MathSciNet  Google Scholar 

  24. Shen, Q.K., Jiang, B., Cocquempot, V.: Adaptive fuzzy observer-based active fault-tolerant dynamic surface control for a class of nonlinear systems with actuator faults. IEEE Trans. Fuzzy Syst 22(2), 338–349 (2014)

    Article  Google Scholar 

  25. Wang, Y.C., Chien, C.J.: An observer-based model reference adaptive iterative learning controller for nonlinear systems. Int. J.Fuzzy Syst. 16(1), 73–85 (2014)

    MathSciNet  Google Scholar 

  26. Zhang, L.L., Tong, S.C., Li, Y.M.: Adaptive fuzzy output-feedback control with prescribed performance for uncertain nonlinear systems. Int. J. Fuzzy Syst. 16(2), 212–221 (2014)

    Article  MathSciNet  Google Scholar 

  27. Kim, S.H.: Nonquadratic H ∞ stabilization conditions for observer-based T–S fuzzy control systems. IEEE Trans. Fuzzy Syst. 22(3), 699–706 (2014)

    Article  Google Scholar 

  28. Xie, L.: Output feedback H ∞ control of systems with parameter uncertainty. Int. J. Control 63, 741–750 (1996)

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (61433004, 61273027), Science and Technology planning project of Liaoning Province, China (2013219005), and IAPI Fundamental Research Funds 2013ZCX14. This work was supported also by the development project of key laboratory of Liaoning province.

Author information

Author notes

  1. Jianyu Zhang

    Present address: Department of Cultural Foundation, Guidaojiaotong Polytechnic Institute, Shenyang, 110023, Liaoning, China

Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, Liaoning, China

    Yingying Wang & Jianyu Zhang

  2. State Key Laboratory of Synthetical Automation for Process Industries, College of Information Science and Engineering, Northeastern University, Shenyang, 110819, Liaoning, China

    Huaguang Zhang & Yingchun Wang

Authors
  1. Yingying Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huaguang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jianyu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yingchun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huaguang Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y., Zhang, H., Zhang, J. et al. An SOS-Based Observer Design for Discrete-Time Polynomial Fuzzy Systems. Int. J. Fuzzy Syst. 17, 94–104 (2015). https://doi.org/10.1007/s40815-015-0003-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-015-0003-x

Keywords

Search

Navigation