[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Observer-based Adaptive Fuzzy Control for Nonlinear Fractional-Order Systems via Backstepping and Sliding Mode Techniques

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

Abstract

Compared with integral-order calculus, fractional calculus is better at depicting the real process with memory property and history-dependent property. As a result, this work investigates a class of nonlinear strict-feedback fractional-order systems and presents a novel control strategy. To begin, in order to cope with the unknown drift functions and unmeasurable system states, fuzzy logic systems (FLSs)and a robust fractional-order state observer are designed. Second, in order to further reduce the FLS approximation error and state estimation error, a hyperbolic tangent function is implemented. Third, the problem of the differential explosion caused by repeated differentiation when employing the backstepping technique when designing a control scheme is also overcome without the help of a command filter or dynamic surface control. Finally, theoretical analysis and simulation results show that by combining the backstepping procedure with the sliding mode technique, not only is it possible to achieve strong robustness against unknown drift function and unknown external time-varying disturbance, but also that the tracking error can converge to the vicinity of the origin.

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
£29.99 /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 includes VAT (United Kingdom)

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

Similar content being viewed by others

Explore related subjects

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

References

  1. Li, G., Li, Y., Chen, H., Deng, W.: Fractional-order controller for course-keeping of underactuated surface vessels based on frequency domain specification and improved particle swarm optimization algorithm. Appl. Sci. 12(6), 3139 (2022)

    Article  Google Scholar 

  2. Lai, G., Zhang, Y., Liu, Z., Chen, C.L.P.: Indirect adaptive fuzzy control design with guaranteed tracking error performance for uncertain canonical nonlinear systems. IEEE Trans. Fuzzy Syst. 27(6), 1139–1150 (2019)

    Article  Google Scholar 

  3. Bououden, S., Chadli, M., Karimi, H.R.: An ant colony optimization-based fuzzy predictive control approach for nonlinear processes. Inf. Sci. 299, 143–158 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chang, X.-H., Qiao, M., Zhao, X.: Fuzzy energy-to-peak filtering for continuous-time nonlinear singular system. IEEE Trans. Fuzzy Syst. (2021). https://doi.org/10.1109/TFUZZ.2021.3080978

    Article  Google Scholar 

  5. Chang, X.H.: Robust Output Feedback H-infinity Control and Filtering for Uncertain Linear Systems. Springer, Berlin (2014)

    Book  Google Scholar 

  6. Wang, D., Liu, D., Li, H., Luo, B., Ma, H.: An approximate optimal control approach for robust stabilization of a class of discrete-time nonlinear systems with uncertainties. IEEE Trans. Syst. Man Cybernet. Syst. 46(5), 713–717 (2016)

    Article  Google Scholar 

  7. Wang, D., Ha, M., Qiao, J.: Self-learning optimal regulation for discrete-time nonlinear systems under event-driven formulation. IEEE Trans. Autom. Control 65(3), 1272–1279 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  8. Wang, D., He, H., Liu, D.: Intelligent optimal control with critic learning for a nonlinear overhead crane system. IEEE Trans. Ind. Inf. 14(7), 2932–2940 (2017)

    Article  Google Scholar 

  9. Basin, M.V., Jesus, R.G.: Optimal control for linear systems with multiple time delays in control input. IEEE Trans. Autom. Control 51(1), 91–97 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Wang, L., Basin, M.V., Li, H., Lu, R.: Observer-based composite adaptive fuzzy control for nonstrict-feedback systems with actuator failures. IEEE Trans. Fuzzy Syst. 26(4), 2336–2347 (2017)

    Article  Google Scholar 

  11. Jin, X., Wang, S., Qin, J., Zheng, W.X., Kang, Y.: Adaptive fault-tolerant consensus for a class of uncertain nonlinear second-order multi-agent systems with circuit implementation. IEEE Trans. Circuits Syst. I Regul. Pap. 65(7), 2243–2255 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wang, D., Mu, C., He, H., Liu, D.: Event-driven adaptive robust control of nonlinear systems with uncertainties through NDP strategy. IEEE Trans. Syst. Man Cybernet. Syst. 47(7), 1358–1370 (2016)

    Article  Google Scholar 

  13. Wang, T., Gao, H., Qiu, J.: A combined adaptive neural network and nonlinear model predictive control for multirate networked industrial process control. IEEE Trans. Neural Netw. Learn. Syst. 27(2), 416–425 (2015)

    Article  MathSciNet  Google Scholar 

  14. Sun, W., Gao, H., Yao, B.: Adaptive robust vibration control of full-car active suspensions with electrohydraulic actuators. IEEE Trans. Control Syst. Technol. 21(6), 2417–2422 (2013)

    Article  Google Scholar 

  15. Xing, X., Liu, J.: Vibration and position control of overhead crane with three-dimensional variable length cable subject to input amplitude and rate constraints. IEEE Trans. Syst. Man Cybernet. Syst. 51(7), 4127–4138 (2019)

    Article  Google Scholar 

  16. Zhang, X., Wang, H., Du, C., Fan, X., Cui, L., Chen, H., Deng, F., Tong, Q., He, M., Yang, M., et al.: Custom-molded offloading footwear effectively prevents recurrence and amputation, and lowers mortality rates in high-risk diabetic foot patients: a multicenter, prospective observational study. Diabetes Metab. Syndr. Obes. Targets Therapy 15, 103 (2022)

    Article  Google Scholar 

  17. Deng, W., Li, Z., Li, X., Chen, H., Zhao, H.: Compound fault diagnosis using optimized MCKD and sparse representation for rolling bearings. IEEE Trans. Instrum. Meas. 71, 1–9 (2022)

    Google Scholar 

  18. Deng, W., Zhang, X., Zhou, Y., Liu, Y., Zhou, X., Chen, H., Zhao, H.: An enhanced fast non-dominated solution sorting genetic algorithm for multi-objective problems. Inf. Sci. 585, 441–453 (2022)

    Article  Google Scholar 

  19. Cui, H., Guan, Y., Chen, H.: Rolling element fault diagnosis based on VMD and sensitivity MCKD. IEEE Access 9, 120297–120308 (2021)

    Article  Google Scholar 

  20. Wang, T., Wang, Y., Yang, X., Yang, J.: Further results on optimal tracking control for nonlinear systems with nonzero equilibrium via adaptive dynamic programming. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/TNNLS.2021.3105646

    Article  Google Scholar 

  21. Wei, J., Zhang, Y., Bao, H.: An exploration on adaptive iterative learning control for a class of commensurate high-order uncertain nonlinear fractional order systems. IEEE/CAA J. Autom. Sin. 5(2), 618–627 (2018)

    Article  MathSciNet  Google Scholar 

  22. Ma, Z., Ma, H.J.: Adaptive fuzzy backstepping dynamic surface control of strict-feedback fractional order uncertain nonlinear systems. IEEE Trans. Fuzzy Syst. 28(1), 122–133 (2019)

    Article  Google Scholar 

  23. Boroujeni, E.A., Momeni, H.R.: Observer based control of a class of nonlinear fractional order systems using lmi. Int. J. Sci. Eng. Investig. 1(1), 48–52 (2012)

    Google Scholar 

  24. Ma, X., Sun, Z.: Analysis and design of fuzzy controller and fuzzy observer. IEEE Trans. Fuzzy Syst. 7(1), 769–770 (1998)

    Google Scholar 

  25. Liu, M., Cao, X., Shi, P.: Fuzzy-model-based fault-tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults. IEEE Trans. Fuzzy Syst. 21(5), 789–799 (2013)

    Article  Google Scholar 

  26. Fu, S., Qiu, J., Chen, L., Mou, S.: Adaptive fuzzy observer design for a class of switched nonlinear systems with actuator and sensor faults. IEEE Trans. Fuzzy Syst. 26(6), 3730–3742 (2018)

    Article  Google Scholar 

  27. Tong, S., Li, Y., Shi, P.: Observer-based adaptive fuzzy backstepping output feedback control of uncertain MIMO pure-feedback nonlinear systems. IEEE Trans. Fuzzy Syst. 20(4), 771–785 (2012)

    Article  Google Scholar 

  28. Qiu, J., Sun, K., Wang, T., Gao, H.: Observer-based fuzzy adaptive event-triggered control for pure-feedback nonlinear systems with prescribed performance. IEEE Trans. Fuzzy Syst. 27(11), 2152–2162 (2019)

    Article  Google Scholar 

  29. N’Doye, I., Zasadzinski, M., Darouach, M., Radhy, N.E.: Observer-based control for fractional-order continuous-time system. In: Proceeding IEEE Conference on Decision and Control, Shanghai, P.R.China (2009)

  30. N’Doye, I., Holger, V., Mohamed, D.: Observer-based approach for fractional-order chaotic synchronization and secure communication. IEEE J. Emerg. Sel. Topics Circuits Syst. 3(3), 442–450 (2013)

    Article  Google Scholar 

  31. Ye, X., Jiang, J.: Adaptive nonlinear design without a priori knowledge of control directions. IEEE Trans. Autom. Control 43(11), 1617–1621 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  32. Podlubny, I.: Fractional Differential Equations: an Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Elsevier, New York (1998)

    MATH  Google Scholar 

  33. Dragomir, S.S.: A note on young’s inequality. Rev. Real Acad. Cienc. Exactas Fis. Nat. - A: Mat. 111(2), 1–6 (2016)

    MathSciNet  Google Scholar 

  34. Polycarpou, M.M., Ioannou, P.A.: A robust adaptive nonlinear control design. Automatica 32(3), 423–427 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  35. Li, Y., Chen, Y., Podlubny, I.: Mittag-leffler stability of fractional order nonlinear dynamic systems. Automatica 45(8), 1965–1969 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  36. Podlubny, I.: Geometric and physical interpretation of fractional integration and fractional differentiation. Fract. Calc. Appl. Anal. 5, 367–386 (2001)

    MathSciNet  MATH  Google Scholar 

  37. 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 

  38. Wang, Y., Wang, T., Yang, j., Yang, X.: A novel method to design controller parameters by using uniform design algorithm. arXiv:2012.06803 (2020)

  39. Yang, X., Zheng, X., Gao, H.: SGD-based adaptive NN control design for uncertain nonlinear systems. IEEE Trans. Neural Netw. Learn. Syst. 29(10), 5071–5083 (2018)

    Article  MathSciNet  Google Scholar 

Download references

Funding

This work was supported by the National Natural Science Foundation of China under Grant 61803122 and Grant 61773143, in part by the 111 Project under Grant B16014, in part by the Special Project of Heilongjiang Postdoctoral Science Foundation under Grant LBH-TZ2011, in part by special projects in key fields of Guangdong Provincial Department of Education of China under Grant 2019KZDZX1025, in part by the funding AC01202101103 from Shenzhen Institute of Artificial Intelligence and Robotics for Society, and in part by Shenzhen Peacock Plan of Shenzhen Science and Technology Program (Grant No.KQTD2016113010470345).

Author information

Authors and Affiliations

  1. Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin, 150080, China

    Jiae Yang, Yujia Wang, Tong Wang, Xuebo Yang & Yu Liu

  2. College of Science, Liaoning University of Technology, Jinzhou, 121001, China

    Shuai Sui

  3. School of Intelligent Manufacturing, Wuyi University, Jiangmen, 529020, China

    Fuqin Deng

  4. Shenzhen Institute of Artificial Intelligence and Robotics for Society, Shenzhen, 518000, China

    Fuqin Deng

  5. 3irobotix, Shenzhen, 518000, China

    Fuqin Deng

Authors
  1. Jiae Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yujia Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fuqin Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shuai Sui
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Xuebo Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Yu Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yujia Wang, Fuqin Deng or Xuebo Yang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, J., Wang, Y., Deng, F. et al. Observer-based Adaptive Fuzzy Control for Nonlinear Fractional-Order Systems via Backstepping and Sliding Mode Techniques. Int. J. Fuzzy Syst. 24, 3650–3665 (2022). https://doi.org/10.1007/s40815-022-01353-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-022-01353-5

Keywords

Search

Navigation