Skip to main content
SpringerLink
Log in

Optimal Robust Control for Constrained Fuzzy Dynamic Systems: Semi-infinite Case

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

Abstract

We consider a constrained state and constrained control design problem for fuzzy dynamic systems. The uncertainty in the system is time-varying and bounded, with the bound information prescribed by a fuzzy set. The control input of systems is also constrained to be one-sided (either positive or negative). An optimal design of a robust control is proposed. It is proven that the global solution to an optimal design problem always exists and is unique. Neither the system nor the control is fuzzy heuristic if-then rule-based.

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

Similar content being viewed by others

References

  1. Luenberger, D.G.: Introduction to Dynamic Systems: Theory, Models, and Applications. Wiley, New York (1979)

    MATH  Google Scholar 

  2. Goh, B.S., Leitmann, G., Vincent, T.L.: Optimal control of a prey-predator system. Math. Biosci. 19(3–4), 263–286 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhou, J., Kim, C.G.: Positive solutions for a lotka volterra prey predator model with cross-diffusion of fractional type. Results Math. 65(3–4), 293–320 (2013)

    MathSciNet  MATH  Google Scholar 

  4. Chen, Y.H., Kuo, C.Y.: Positive uncertain systems with one-sided robust control. J. Dyn. Syst. Meas. Control 119(4), 675–684 (1997)

    Article  MATH  Google Scholar 

  5. Garrett, T.K., Steeds, W.: The Motor Vehicle, 13th edn. Society of Automotive Engineers Inc., Warrendale, (2002)

    Google Scholar 

  6. Costaa, M.I.S., Kaszkurewiczb, E., Bhayab, A., Hsub, L.: Achieving global convergence to an equilibrium population in predator-prey systems by the use of a discontinuous harvesting policy. Ecol. Model. 128(2–3), 89–99 (2000)

    Article  Google Scholar 

  7. Kendrick, D.A.: Stochastic Control for Economic Models. McGraw-Hill, New York (1981)

    MATH  Google Scholar 

  8. Huang, J., Chen, Y.H., Cheng, A.G.: Robust control for fuzzy dynamical systems: uniform ultimate boundedness and optimality. IEEE Trans. Fuzzy Syst. 26(6), 1022–1031 (2012)

    Article  MathSciNet  Google Scholar 

  9. Xu, J., Chen, Y.H., Guo, H.: On the foundations of fuzzy dynamical system theory: controllability and observability. Int. J. Fuzzy Syst. 16(4), 497–510 (2014)

    MathSciNet  Google Scholar 

  10. Chen, Y.H.: Optimal design of robust control for uncertain systems: a fuzzy approach. Nonlinear Dyn. Syst. Theor. 1(2), 133–143 (2001)

    MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  12. Ho, W.H., Tsai, J.T., Chou, J.H.: Robust quadratic-optimal control of TS-fuzzy-model-based dynamic systems with both elemental parametric uncertainties and norm-bounded approximation error. IEEE Trans. Fuzzy Syst. 17(3), 518–531 (2009)

    Article  Google Scholar 

  13. Chang, J.W., Wang, R.J., Wang, W.J., Huang, C.H.: Implementation of an object-grasping robot arm using stereo vision measurement and fuzzy control. Int. J. Fuzzy Syst. 17(2), 193–205 (2015)

    Article  Google Scholar 

  14. Yang, C.H., Wu, C.L., Chen, Y.J., Shiao, S.H.: Reduced fuzzy controllers for lorenz stenflo system control and synchronization. Int. J. Fuzzy Syst. 17(2), 158–169 (2015)

    Article  MathSciNet  Google Scholar 

  15. Mamdani, E.H.: Application of fuzzy algorithms for control of simple dynamic plant. Proc. Inst. Electr. Eng. 121(12), 1585–1588 (1974)

    Article  Google Scholar 

  16. Hwang, C.L.: Decentralized fuzzy control of nonlinear interconnected dynamic delay systems via mixed \(H_2\)/\(H_{\infty }\). IEEE Trans. Fuzzy Syst. 19(2), 276–290 (2011)

    Article  Google Scholar 

  17. Barmish, B.R., Leitmann, G.: On ultimate boundedness control of uncertain systems in the absence of matching assumptions. IEEE Trans. Autom. Control 27(1), 153–158 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  18. Corless, M.J., Leitmann, G.: Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems. IEEE Trans. Autom. Control 26(5), 1139–1144 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  19. Chen, Y.H.: A new approach to the control design of fuzzy dynamical systems. ASME J. Dyn. Syst. Meas. Control 133(6), 2417–2424 (2011)

    Google Scholar 

  20. Zhao, R., Chen, Y.H., Jiao, S.: Optimal design of robust control for positive fuzzy dynamic systems with one-sided control constraint. J. Intell. Fuzzy Syst. 8, 43–62 (2015)

    Google Scholar 

  21. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prectice-Hall, Upper Saddle River (1995)

    MATH  Google Scholar 

  22. Xu, J., Chen, Y.H., Guo, H.: Fractional robust control design for fuzzy dynamical systems: an optimal approach. J. Intell. Fuzzy Syst. 29(2), 553–569 (2015)

    Article  MathSciNet  Google Scholar 

  23. Zhen, S., Huang, K., Sun, H., Zhao, H., Chen, Y.H.: Optimal robust control for rigid serial manipulators: a fuzzy approach. Asian J. Control 17(6), 2329–2344 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  24. Zhao, R., Chen, Y.H., Jiao, S.: Optimal design of constraint-following control for fuzzy mechanical systems. IEEE Trans. Fuzzy Syst. (2015). doi:10.1109/TFUZZ.2015.2502275

  25. Picart, D., Milner, F.: Optimal control in a multistage physiologically structured insect population model. Appl. Mech. Comput. 247, 573–588 (2014)

    MathSciNet  MATH  Google Scholar 

  26. Du, J., Huang, T., Sheng, Z., Zhang, H.: A new method to control chaos in an economic system. Appl. Mech. Comput. 217(6), 2370–2380 (2010)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

Ruiying Zhao is supported by the China Fundamental Research Funds for the Central Universities (No. 0009-2014G1251024) and (No. 310825161009). Shengjie Jiao is supported by the National Science and Technology Pillar Program (No. 2015BAF07B08).

Author information

Authors and Affiliations

  1. National Engineering Laboratory for Highway Maintenance Equipment, Chang’an University, Xi’an, 710065, Shaanxi, People’s Republic of China

    Ruiying Zhao & Shengjie Jiao

  2. The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Ye-Hwa Chen

Authors
  1. Ruiying Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ye-Hwa Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shengjie Jiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ye-Hwa Chen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, R., Chen, YH. & Jiao, S. Optimal Robust Control for Constrained Fuzzy Dynamic Systems: Semi-infinite Case. Int. J. Fuzzy Syst. 18, 557–569 (2016). https://doi.org/10.1007/s40815-016-0169-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-016-0169-x

Keywords

Search

Navigation