Skip to main content
SpringerLink
Log in

Adaptive Fixed-Time Fuzzy Control of Uncertain Nonlinear Quantized Systems

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

Abstract

This article settles the issue of adaptive fixed-time control of uncertain nonlinear quantized systems. Different from the traditional study about fixed-time control for uncertain nonlinear systems, quantitative control issue is considered in this paper, and the nonlinear term can be unknown. The new adaptive control tactic of fixed-time tracking control is proposed via fuzzy logic systems approaching unknown nonlinearity, which overcomes the existing limitation of the upper boundary of system settling time relies on the initial condition. The closed-loop system stability is guaranteed in a fixed time. At the end of this paper, the availability of the strategy is proved by a numerical simulation.

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

Similar content being viewed by others

References

  1. Miller, R.K., Michel, A.N., Farrel, J.A.: Quantizer effects on steady state error specifications of digital control systems. IEEE Trans. Automat. Control. 34(6), 651–654 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  2. Wong, W., Brockett, R.W.: Systems with finite communication bandwidth constraints II: Stabilization with limited information feedback. IEEE Trans. Automat. Control. 44(5), 1049–1053 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  3. Jan, L., Bernhard, N., Schroder, J.: Deterministic discrete-event representations of linear continuous variable systems. Automatica. 35(3), 395–406 (1999)

    Article  MathSciNet  Google Scholar 

  4. Ishii, H., Francis, B.: Limited Data Rate in Control Systems With Network. Springer, Berlin (2002)

    MATH  Google Scholar 

  5. Tatikonda, S., Mitter, S.: Control under communication constraints. IEEE Trans. Automat. Control. 49(7), 1056–1068 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gao, H.J., Chen, T.W.: A new approach to quantized feedback control systems. Automatica. 44(9), 534–542 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Elia, N., Mitter, S.: Stabilization of linear systems with limited information. IEEE Trans. Automat. Control. 46(9), 1384–1400 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  8. Liu, J., Elia, N.: Quantized feedback stabilization of non-linear affine systems. J. Int. J. Control. 77(3), 239–249 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Nair, G., Evans, R.: Stabilizability of stochastic linear systems with finite feedback data rates. SIAM J. Control Optim. 43(2), 413–436 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Persis, C.D., Isidori, A.: Stabilizability by state feedback implies stabilizability by encoded state feedback. Syst. Control Lett. 53(3–4), 249–258 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Liberzon, D., Hespanha, J.: Stabilization of nonlinear systems with limited information feedback. IEEE Trans. Automat. Control. 50(6), 910–915 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Liang, H., Guo, X., Pan, Y., Huang, T.: Event-triggered fuzzy bipartite tracking control for network systems based on distributed reduced-order observers. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.2982618

    Article  Google Scholar 

  13. Wang, W., Liang, H., Pan, Y., Li, T.: Prescribed performance adaptive fuzzy containment control for nonlinear multi-agent systems using disturbance observer. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.2969499

    Article  Google Scholar 

  14. Zhu, Z., Pan, Y., Zhou, Q., Lu, C.: Event-triggered adaptive fuzzy control for stochastic nonlinear systems with unmeasured states and unknown backlash-like hysteresis. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.2973950

    Article  Google Scholar 

  15. Zhou, Q., Zhao, S., Li, H., Lu, R., Wu, C.: Adaptive neural network tracking control for robotic manipulators with dead-zone. IEEE Trans. Neural Netw. Learn. Syst. 30(12), 3611–3620 (2019)

    Article  MathSciNet  Google Scholar 

  16. Tang, Y.: Terminal sliding mode control for rigid robots. Automatica. 34(1), 51–56 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  17. Tan, C.P., Yu, X., Man, Z.: Terminal sliding mode observers for a class of nonlinear systems. Automatica. 46(8), 1401–1404 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. Jiang, B., Karimi, H.R., Kao, Y., Gao, C.: Takagi–Sugeno model based event-triggered fuzzy sliding-mode control of networked control systems with semi-Markovian switchings. IEEE Trans. Fuzzy Syst. 28(4), 673–683 (2020)

    Article  Google Scholar 

  19. Jiang, B., Karimi, H.R., Yang, S., Gao, C.C., Kao, Y.: Observer-based adaptive sliding mode control for nonlinear stochastic Markov jump systems via T-S fuzzy modeling: applications to robot arm model. IEEE Trans. Ind. Electron. 99, 1 (2020)

    Google Scholar 

  20. Bhat, S.P., Bernstein, D.S.: Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Automat. Control. 43(5), 678–682 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  21. Bhat, S.P., Bernstein, D.S.: Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38(3), 751–766 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  22. Huang, X., Lin, W., Yang, B.: Global finite-time stabilization of a class of uncertain nonlinear systems. Automatica. 41(5), 881–888 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  23. Du, P., Pan, Y., Li, H., Lam, H.-K.: Nonsingular finite-time event-triggered fuzzy control for large-scale nonlinear systems. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.2992632

    Article  Google Scholar 

  24. Qi, W., Gao, M., Ahn, C.K., Cao, J., Cheng, J., Zhang, L.: Quantized fuzzy finite-time control for nonlinear semi-Markov switching systems. Exp. Briefs II IEEE Trans. Circuits Syst. II (2019). https://doi.org/10.1109/TCSII.2019.2962250

    Article  Google Scholar 

  25. Yang, D., Cai, K.: Finite-time quantized guaranteed cost fuzzy control for continuous-time nonlinear systems. Exp. Systems Appl. 37(10), 6963–6967 (2010)

    Article  Google Scholar 

  26. Qi, X., Liu, W., Yang, Y., Lu, J.: Adaptive finite-time fuzzy control for nonlinear systems with input quantization and unknown time delays. J. Franklin Inst. (2020). https://doi.org/10.1002/acs.3146

    Article  MathSciNet  MATH  Google Scholar 

  27. Polyakov, A.: Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans. Automat. Control. 57(8), 2106–2110 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  28. Zhu, Y., Zheng, W.X.: Multiple Lyapunov functions analysis approach for discrete-time switched piecewise-affine systems under dwell-time constraints. IEEE Trans. Automat. Control. 65(5), 2177–2184 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  29. Zhu, Y., Zheng, W.X., Zhou, D.: Quasi-synchronization of discrete-time Lur’e-type switched systems with parameter mismatches and relaxed PDT constraints. IEEE Trans. Cybern. 50(5), 2026–2037 (2020)

    Article  Google Scholar 

  30. Zhu, Y., Zheng, W.X.: Observer-based control for cyber-physical systems with DoS attacks via a cyclic switching strategy. IEEE Trans. Automat. Control. 65(8), 3714–3721 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  31. Li, J., Yang, Y., Hua, C., Guan, X.: Fixed-time backstepping control design for high-order strict feedback nonlinear systems via terminal sliding mode. IET Control Theory Appl. 11(8), 1184–1193 (2017)

    Article  MathSciNet  Google Scholar 

  32. Hua, C.C., Li, Y.F., Guan, X.P.: Finite/fixed-time stabilization for nonlinear interconnected systems with dead-zone input. IEEE Trans. Automat. Control. 62(5), 2554–2560 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  33. Yang, H., Ye, D.: Fixed-time stabilization of uncertain strict-feedback nonlinear systems via a bi-limit-like strategy. Int. J. Robust Nonlinear Control (2018). https://doi.org/10.1002/rnc.4328

    Article  MathSciNet  MATH  Google Scholar 

  34. Ba, D., Li, Y.X., Tong, S.: Fixed-time adaptive neural tracking control for a class of uncertain nonstrict nonlinear systems. Neurocomputing. 363, 273–280 (2019)

    Article  Google Scholar 

  35. Zuo, Z.Y.: Non-singular fixed-time terminal sliding mode control of non-linear systems. IET Control Theory Appl. 9(4), 545–552 (2014)

    Article  MathSciNet  Google Scholar 

  36. Zuo, Z.Y.: Nonsingular fixed-time consensus tracking for second-order multi-agent networks. Automatica. 54, 305–309 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  37. Ni, J., Liu, L., Liu, C., Hu, X., Li, S.: Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system. IEEE Trans. Circuits Syst. II 64(2), 151–155 (2017)

    Article  Google Scholar 

  38. Sun, H., Hou, L., Zong, G., Yu, X.: Fixed-time attitude tracking control for spacecraft with input quantization. IEEE Trans. Aerospace Electron. Syst. 55(1), 124–134 (2018)

    Article  Google Scholar 

  39. Chen, M., An, S.Y.: Fixed-time tracking control for strict-feedback nonlinear systems based on backstepping algorithm. Control Decis. (2019). https://doi.org/10.1155/2020/8887925

    Article  Google Scholar 

  40. Wang, L.X.: Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Prentice-Hall, Englewood Cliffs (1994)

    Google Scholar 

  41. Qian, C., Lin, W.: Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Syst. Control Lett. 42(3), 185–200 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  42. Wang, F., Zhang, X.: Adaptive finite time control of nonlinear systems under time-varying actuator failures. IEEE Trans. Syst. Man Cybern. 49(9), 1845–1852 (2019)

    Article  Google Scholar 

  43. Persis, C.D., Mazenc, F.: Stability of quantized time-delay nonlinear systems: a Lyapunov-Krasowskii-functional approach, Mathematics of Control. Signals Syst. 21(4), 337–370 (2010)

    Article  MATH  Google Scholar 

  44. Zhou, J., Wen, C.Y., Yang, G.H.: Adaptive backstepping stabilization of nonlinear uncertain systems with quantized input signal. IEEE Trans. Automat. Control. 59(2), 460–464 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  45. Liu, Z., Wang, F., Zhang, Y., Chen, C.L.P.: Fuzzy adaptive quantized control for a class of stochastic nonlinear uncertain systems. IEEE Trans. Cybern. 46(2), 524–534 (2016)

    Article  Google Scholar 

  46. Deng, H., Krstic, M.: Stochastic nonlinear stabilization. Part I: a backstepping design. Syst. Control Lett. 32(3), 143–150 (1997)

    Article  MATH  Google Scholar 

  47. Wang, F., Liu, Z., Zhang, Y., Chen, C.L.P.: Adaptive quantized fuzzy control of stochastic nonlinear systems with actuator dead-zone. Inf. Sci. 370–371, 385–401 (2016)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Pengxu Ren & Fang Wang

  2. Department of mathematics, Xi’an Jiaotong-Liverpool University, Xi’an, 215123, China

    Ruitai Zhu

Authors
  1. Pengxu Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ruitai Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fang Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ren, P., Wang, F. & Zhu, R. Adaptive Fixed-Time Fuzzy Control of Uncertain Nonlinear Quantized Systems. Int. J. Fuzzy Syst. 23, 794–803 (2021). https://doi.org/10.1007/s40815-020-01018-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-020-01018-1

Keywords

Search

Navigation