Skip to main content
Springer Nature Link
Log in

Finite-Time Command Filter-Based Adaptive NN Control for MIMO Nonlinearly Parameterized Systems with Time-Varying Input Delay

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

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

This paper studies the issue problem of adaptive neural tracking control for multi-input and multi-output (MIMO) nonlinearly parameterized systems with time-varying input delay and unknown disturbances. The integrator with parameters is added to successfully eliminate the influence of time-varying input delay in the process of coordinate changes. The finite-time command filter is adopted to solve the issues of “explosion of complexity” and the error compensation mechanism is introduced to deal with the filtered error. The neural networks (NNs) are applied to approximate the unknown nonlinearly parameterized functions. Then, based on the minimal learning parameters (MLP) algorithm, a new adaptive NN backstepping control scheme is developed and only two adaptive parameters need to be adjusted online in the controller design procedure. Moreover, this proposed method can guarantee that the stability of the overall MIMO closed-loop system and the tracking error converge to be arbitrarily small within a finite time. Finally, the simulation example has evaluated the validity of the control method.

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
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Explore related subjects

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

References

  1. Liu, Y.J., Lu, S.M., Tong, S.C.: Neural network controller design for an uncertain robot with time-varying output constraint. IEEE Trans. Syst. Man Cybernet. 47(8), 2060–2068 (2017)

    Article  Google Scholar 

  2. Nai, Y.Q., Yang, Q.Y., Wu, Z.: Prescribed performance adaptive neural compensation control for intermittent actuator faults by state and output feedback. IEEE Trans. Neural Netw. (2020). https://doi.org/10.1109/TNNLS.2020.3026208

    Article  Google Scholar 

  3. Han, H., Wu, X., Qiao, J.: Nonlinear systems modeling based on self-organizing fuzzy-neural-network with adaptive computation algorithm. IEEE Trans. Cybern. 44(4), 554–564 (2014)

    Article  Google Scholar 

  4. Zhang, J., Yang, G.: Fuzzy adaptive output feedback control of uncertain nonlinear systems with prescribed performance. IEEE Trans. Cybern. 48(5), 1342–1354 (2018)

    Article  Google Scholar 

  5. Nai, Y.Q., Yang, Q.Y., Zhang, Z.Q.: Adaptive neural output feedback compensation control for intermittent actuator faults using command-filtered backstepping. IEEE Trans. Neural Netw. 31(9), 3497–3511 (2020)

    Article  MathSciNet  Google Scholar 

  6. Cui, G.Z., Yang, W., Yu, J.P.: Neural network-based finite-time adaptive tracking control of nonstrict-feedback nonlinear systems with actuator failures. Inf. Sci. 545(4), 298–311 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  7. Liu, Y.C., Zhu, Q.D.: Adaptive neural network finite-time tracking control of full state constrained pure feedback stochastic nonlinear systems. J. Frankl. Inst. 357(11), 6738–6759 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  8. Zha, W.T., Zhai, J.Y., Fei, S.M., Wang, Y.J.: Finite-time stabilization for a class of stochastic nonlinear systems via output feedback. Isa Trans. 53(3), 709–716 (2014)

    Article  Google Scholar 

  9. Liu, Y., Liu, X.P., Jing, Y.W.: Adaptive neural networks finite-time tracking control for non-strict feedback systems via prescribed performance. Inf. Sci. 468, 29–46 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zouari, F., Ibeas, A., Boulkrouned, A., Cao, J., Arefi, M.M.: Neural network controller design for fractional-order systems with input nonlinearities and asymmetric time-varying pseudo-state constraints. Chaos Solitons Fract. (2021). https://doi.org/10.1016/j.chaos.2021.110742

    Article  MathSciNet  Google Scholar 

  11. Li, Y.M., Li, K.W., Tong, S.C.: Finite-time adaptive fuzzy output feedback dynamic surface control for mimo non-strict feedback systems. IEEE Trans. Fuzzy Syst. 27(1), 96–110 (2019)

    Article  MathSciNet  Google Scholar 

  12. Wu, Y., Pan, Y.N., Chen, M., Li, H.Y.: Quantized adaptive finite-time bipartite NN tracking control for stochastic multiagent systems. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.3008020

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  14. Haimo, V.T.: Finite time controllers. SIAM J. Control Optim. 24(4), 760–770 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  15. Hong, Y., Huang, J., Xu, Y.S.: On an output feedback finite-time stabilization problem. IEEE Trans. Autom. Control 46(2), 305–309 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. Zhu, Z., Xia, Y.Q., Fu, M.Y.: Attitude stabilization of rigid spacecraft with finite-time convergence. Int. J. Robust Nonlinear Control 21(6), 686–702 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Si, W.J., Wang, D.S.: Finite-time decentralized adaptive neural constrained control for interconnected nonlinear time-delay systems with dynamics couplings among subsystems. ISA Trans. 80, 54–64 (2018)

    Article  Google Scholar 

  18. Zhang, J., Xia, J.W., Sun, W., Zhuang, G.M., Wang, Z.: Finite-time tracking control for stochastic nonlinear systems with full state constraints. Appl. Math. Comput. 338, 207–220 (2018)

    MathSciNet  MATH  Google Scholar 

  19. Zhao, N.N., Wu, L.B., Ouyang, X.Y., Yan, Y., Zhang, R.Y.: Finite-time adaptive fuzzy tracking control for nonlinear systems with disturbances and dead-zone nonlinearities. Appl. Math. Comput. 362(1), 124–494 (2019)

    MathSciNet  MATH  Google Scholar 

  20. Wang, Y.C., Zhang, J.X., Zhang, H.G., Xie, X.P.: Finite-time adaptive neural control for nonstrict-feedback stochastic nonlinear systems with input delay and output constraints. Appl. Math. Comput. (2020). https://doi.org/10.1016/j.amc.2020.125756

    Article  MATH  Google Scholar 

  21. Wang, F., Liu, Z., Li, X.H., Zhang, Y., Chen, C.L.P.: Observer-based finite time control of nonlinear systems with actuator failures. Inf. Sci. 500, 1–14 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  22. Wang, F., Zhang, L.L., Zhou, S.W., Huang, Y.Y.: Neural network-based finite-time control of quantized stochastic nonlinear systems. Neurocomputing 362, 195–202 (2019)

    Article  Google Scholar 

  23. Rashad, R., Aboudonia, A., Ei-Badawy, A.: A novel disturbance observer-based backstepping controller with command filtered compensation for a MIMO system. J. Frankl. Inst. 353(16), 4039–4061 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  24. Nai, Y.Q., Yang, Q.Y., Zhang, Z.Q.: Adaptive neural output feedback compensation control for intermittent actuator faults using command-filtered backstepping. IEEE Trans. Neural Netw. Learn. Syst. 31(9), 3497–3511 (2020)

    Article  MathSciNet  Google Scholar 

  25. Yu, J.P., Zhao, L., Yu, H.S., Lin, C., Dong, W.J.: Fuzzy finite-time command filtered control of nonlinear systems with input saturation. IEEE Trans. Cybern. 12(15), 2148–2155 (2017)

    Google Scholar 

  26. Li, Y.X.: Finite time command filtered adaptive fault tolerant control for a class of uncertain nonlinear systems. Automatica 106, 117–123 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  27. Zhang, J., Xia, J., Sun, W., Wang, Z., Shen, H.: Command filter-based finite-time adaptive fuzzy control for nonlinear systems with uncertain disturbance. J. Frankl. Inst. 356(18), 11270–11284 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  28. Liu, J.D., Niu, B., Kao, Y.G., Zhao, P., Yang, D.: Decentralized adaptive command filtered neural tracking control of large-scale nonlinear systems: an almost fast finite-time framework. IEEE Trans. Neural Netw. (2020). https://doi.org/10.1109/TNNLS.2020.3015847

    Article  Google Scholar 

  29. Fu, C., Wang, Q.G., Yu, J., Lin, C.: Neural Network-Based Finite-Time Command Filtering Control for Switched Nonlinear Systems With Backlash-Like Hysteresis. IEEE Trans. Neural Netw. (2020). https://doi.org/10.1109/TNNLS.2020.3009871

    Article  Google Scholar 

  30. Levant, A.: High-order sliding modes, differentiation and output feedback control. Int. J. Control 76(9), 427–434 (2003)

    MathSciNet  MATH  Google Scholar 

  31. 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 

  32. Obuz, S., Klotz, J.R., Kamalapurkar, R., Dixon, W.: Unknown time-varying input delay compensation for uncertain nonlinear systems. Automatica 76, 222–229 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  33. Zha, W.T., Zhai, J.Y., Fei, S.: Global output feedback control for a class of high-order feedforward nonlinear systems with input delay. Isa Trans. 52(4), 494–500 (2013)

    Article  Google Scholar 

  34. Li, H.Y., Wang, L.J., Du, H.P., Abdesselem, B.: Adaptive fuzzy backstepping tracking control for strict-feedback systems with input delay. IEEE Trans. Fuzzy Syst. 25(3), 642–652 (2017)

    Article  Google Scholar 

  35. Yang, Z.J., Zhang, X.Y., Zong, X.J., Wang, G.G.: Adaptive fuzzy control for non-strict feedback nonlinear systems with input delay and full state constraints. J. Frankl. Inst. 357(11), 6658–6681 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  36. Wei, Y.S., Lin, Z.L.: Time-varying low gain feedback for linear systems with unknown input delay. Syst. Control Lett. 44123, 98–107 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  37. Li, Y.D., Chen, B., Lin, C., Shang, Y.: Adaptive neural decentralized output-feedback control for nonlinear large-scale systems with input time-varying delay and saturation. Neurocomputing 427(12), 212–224 (2020)

    Google Scholar 

  38. Khazaee, M., Markazi, A.H.D., Omidi, E.: Adaptive fuzzy predictive sliding control of uncertain nonlinear systems with bound-known input delay. Isa Trans. 59, 314–324 (2015)

    Article  Google Scholar 

  39. Zhao, X.D., Yang, H.J., Karimi, H.R., Zhu, Y.Z.: Adaptive neural control of MIMO nonstrict-feedback nonlinear systems with time delay. IEEE Trans. Cybern. 46(6), 1337–1349 (2016)

    Article  Google Scholar 

  40. Homayoun, B., Arefi, M.M., Vafamand, N., Yin, S.: Neuro-adaptive command filter control of stochastic time-delayed nonstrict-feedback systems with unknown input saturation. J. Frankl. Inst. 357(12), 7456–7482 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  41. Huang, J.T., Law, Y.C.: Adaptive linearizing fuzzy control of delayed MIMO nonstrict-feedback systems. IEEE Trans. Fuzzy Syst. 28(10), 2592–2604 (2019)

    Article  Google Scholar 

  42. Wei, J.M., Zhang, Y.A., Sun, M.M., Geng, B.L.: Adaptive iterative learning control of a class of nonlinear time-delay systems with unknown backlash-like hysteresis input and control direction. Isa Trans. 70, 79–92 (2017)

    Article  Google Scholar 

  43. Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities. Cambridge University Press, Cambridge (1952)

    MATH  Google Scholar 

  44. Yue, H.Y., Wei, Z., Chen, Q.J., Zhang, X.Y.: Dynamic surface control for a class of nonlinearly parameterized systems with input time delay using neural network. J. Frankl. Inst. 357(4), 1961–1986 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  45. Yue, H.Y., Yu, S.Q.: Adaptive fuzzy tracking control for a class of stochastic nonlinearly parameterized systems with distributed input delay. J. Frankl. Inst. 353(3), 713–734 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  46. Dong, W., Farrell, J.A., Polycarpou, M.M., Djapic, V., Sharma, M.: Command filtered adaptive backstepping. IEEE Trans. Control Syst. Technol. 20(3), 566–580 (2012)

    Article  Google Scholar 

Download references

Acknowledgements

The project was supported by the Special Fund of the National Natural Science Foundation of China (Grant No.: 11626183), the Postdoctoral Science Foundation of China (Grant No.: 2018M633476), Shaanxi Province Natural Science Fund of China (Grant No.: 2020JM-490), the Youth Talent Promotion Program of Shaanxi Association for Science and Technology (Grant No.: 20180505), the Scientific Research Plan Projects of Shaanxi Education Department (Grant No.: 19JK0466), and the Science Foundation of Xi’an University of Architecture and Technology (Grant No.: ZR18037).

Author information

Authors and Affiliations

  1. School of Science, Xi’an University of Architecture and Technology, Xi’an, 710055, China

    Hongyun Yue, Wufei Zhang & Qingjiang Chen

Authors
  1. Hongyun Yue
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Wufei Zhang
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Qingjiang Chen
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Qingjiang Chen.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yue, H., Zhang, W. & Chen, Q. Finite-Time Command Filter-Based Adaptive NN Control for MIMO Nonlinearly Parameterized Systems with Time-Varying Input Delay. Int. J. Fuzzy Syst. 25, 816–830 (2023). https://doi.org/10.1007/s40815-022-01405-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-022-01405-w

Keywords