Skip to main content

Advertisement

Springer Nature Link
Log in

Disturbance-observer-based adaptive dynamic surface control for nonlinear systems with input dead-zone and delay using neural networks

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Disturbance-observer-based adaptive neural control approach is proposed for nonlinear systems. Considering the effect caused by long input delay and dead-zone, a novel auxiliary system has been introduced to degrade the design difficult. Based on the auxiliary system, a novel disturbance observer is developed to estimate the unknown time-varying external disturbance and the approximation error. What is more, the priori knowledge on the boundary of the disturbance and approximation error is not required for the disturbance observer. The “explosion of complexity” problem has been overcome by using dynamic surface control (DSC) scheme. By combing DSC scheme with backstepping technique, an adaptive neural dynamic surface controller is correctly devised to improve the disturbance rejection performance of the closed-loop system. Finally, the simulations of two examples show the superiority of the proposed scheme.

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
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Explore related subjects

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

References

  1. Mayne D (2002) Nonlinear and adaptive control design. IEEE Trans Autom Contr 41(12):1849

    Article  Google Scholar 

  2. Chang XH, Xiong J, Li ZM et al (2017) Quantized static output feedback control for discrete-time systems. IEEE Trans Ind Info 14(8):3426–3435

    Article  Google Scholar 

  3. Zou W, Shi P, Xiang Z et al (2020) Finite-time consensus of second-order switched nonlinear multi-agent systems. IEEE Trans Neur Netw Learn Sys 31(5):1757–1762

    Article  Google Scholar 

  4. Qi W, Gao X, Ahn CK et al (2022) Fuzzy integral sliding-mode control for nonlinear semi-Markovian switching systems with application. IEEE Trans Sys, Man Cybern: Sys 52(3):1674–1683

    Article  Google Scholar 

  5. Li S, Ahn CK, Xiang Z (2019) Sampled-data adaptive output feedback fuzzy stabilization for switched nonlinear systems with asynchronous switching. IEEE Trans Fuzzy Sys 27(1):200–205

    Article  Google Scholar 

  6. Tong S, Min X, Li Y (2020) Observer-based adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown control gain functions. IEEE Trans Cybern 50(9):3903–3913

    Article  Google Scholar 

  7. Wang X, Niu B, Song X et al (2021) Neural networks-based adaptive practical preassigned finite-time fault tolerant control for nonlinear time-varying delay systems with full state constraints. Int J Rob Nonlin Contr 31(5):1497–1513

    Article  Google Scholar 

  8. Liu Y, Zhu Q, Wen G (2022) Adaptive Tracking Control for Perturbed Strict-Feedback Nonlinear Systems Based on Optimized Backstepping Technique. IEEE Trans Neur Netw Learn Sys 33(2):853–865

    Article  Google Scholar 

  9. Wang H, Liu PX, Xie X et al (2021) Adaptive fuzzy asymptotical tracking control of nonlinear systems with unmodeled dynamics and quantized actuator. Info Sci 575:779–792

    Article  Google Scholar 

  10. Li Y, Liu Y, Tong S (2021) Observer-based neuro-adaptive optimized control of strict-feedback nonlinear systems with state constraints. IEEE Trans Neur Netw Learn Sys. https://doi.org/10.1109/TNNLS.2021.3087796

    Article  Google Scholar 

  11. Swaroop D, Gerdes JC, Yip PP et al (1997) Dynamic surface control of nonlinear systems. Am Contr Conf 5:3028–3034

    Article  Google Scholar 

  12. Chen M, Tao G, Jiang B (2014) Dynamic surface control using neural networks for a class of uncertain nonlinear systems with input saturation. IEEE Trans Neur Netw Learn Sys 26(9):2086–2097

    Article  Google Scholar 

  13. Wang H, Xu K, Liu PX et al (2021) Adaptive fuzzy fast finite-time dynamic surface tracking control for nonlinear systems. IEEE Trans Circ Sys I: Regular Pap 68(10):4337–4348

    Google Scholar 

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

    Article  Google Scholar 

  15. Sun K, Liu L, Qiu J et al (2021) Fuzzy adaptive finite-time fault-tolerant control for strict-feedback nonlinear systems. IEEE Trans Fuzzy Sys 29(4):786–796

    Article  Google Scholar 

  16. Zhao J, Li X, Tong S (2020) Fuzzy adaptive dynamic surface control for strict-feedback nonlinear systems with unknown control gain functions. Int J Sys Sci 1:1–16

    Google Scholar 

  17. Sun K, Qiu J, Karimi HR et al (2021) Event-triggered robust fuzzy adaptive finite-time control of nonlinear systems with prescribed performance. IEEE Trans Fuzzy Sys 29(6):1460–1471

    Article  Google Scholar 

  18. Yan X, Chen M, Feng G et al (2019) Fuzzy robust constrained control for nonlinear systems with input saturation and external disturbances. IEEE Trans Fuzzy Sys 29(2):345–356

    Article  Google Scholar 

  19. Min H, Xu S, Fei S et al (2021) Observer-based NN control for nonlinear systems with full-state constraints and external disturbances. IEEE Trans Neur Netw Learn Sys. https://doi.org/10.1109/TNNLS.2021.3056524

    Article  Google Scholar 

  20. Li K, Tong S (2019) Fuzzy adaptive practical finite-time control for time delays nonlinear systems. Int J Fuzzy Sys 21(4):1013–1025

    Article  Google Scholar 

  21. Liu Y, Liu X, Jing Y et al (2019) Direct adaptive preassigned finite-time control with time-delay and quantized input using neural network. IEEE Trans Neur Netw Learn Sys 31(4):1222–1231

    Article  Google Scholar 

  22. Wang H, Kang S, Zhao X et al (2021) Command filter-based adaptive neural control design for nonstrict-feedback nonlinear systems with multiple actuator constraints. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2021.3079129

    Article  Google Scholar 

  23. Xu Q, Wang Z, Zhen Z (2019) Adaptive neural network finite time control for quadrotor UAV with unknown input saturation. Nonlin Dyn 98(3):1973–1998

    Article  MATH  Google Scholar 

  24. Nakao M, Ohnishi K, Miyachi K (1987) A robust decentralized joint control based on interference estimation. IEEE Int Conf Robot Automat 4:326–331

    Google Scholar 

  25. Xu B, Zhang L, Ji W (2021) Improved non-singular fast terminal sliding mode control with disturbance observer for PMSM drives. IEEE Trans Transport Electrif 7(4):2753–2762

    Article  Google Scholar 

  26. Liu X, Yu H (2021) Continuous adaptive integral-type sliding mode control based on disturbance observer for PMSM drives. Nonli Dyn 104(2):1429–1441

    Article  Google Scholar 

  27. Zhang J, Liu X, Xia Y et al (2016) Disturbance observer-based integral sliding-mode control for systems with mismatched disturbances. IEEE Trans Ind Electr 63(11):7040–7048

    Article  Google Scholar 

  28. Zhang H, Wei X, Zhang L et al (2017) Disturbance rejection for nonlinear systems with mismatched disturbances based on disturbance observer. J Frankl Instit 354(11):4404–4424

    Article  MATH  Google Scholar 

  29. Wei XJ, Wu ZJ, Karimi HR (2016) Disturbance observer-based disturbance attenuation control for a class of stochastic systems. Automatica 63:21–25

    Article  MATH  Google Scholar 

  30. Wei XJ, Dong L, Zhang H et al (2019) Adaptive disturbance observer-based control for stochastic systems with multiple heterogeneous disturbances. Int J Robust Nonlin Contr 29(16):5533–5549

    Article  MATH  Google Scholar 

  31. Zhao Z, Ren Y, Mu C et al (2021) Adaptive neural-network-based fault-tolerant control for a flexible string with composite disturbance observer and input constraints. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2021.3090417

    Article  Google Scholar 

  32. Qiu J, Wang T, Sun K et al (2022) Disturbance observer-based adaptive fuzzy control for strict-feedback nonlinear systems with finite-time prescribed performance. IEEE Trans Fuzzy Sys 30(4):1175–1184

    Article  Google Scholar 

  33. Chen M, Tao G, Jiang B (2015) Dynamic surface control using neural networks for a class of uncertain nonlinear systems with input saturation. IEEE Trans Neur Netw Learn Sys 26:2086–2097

    Article  Google Scholar 

  34. Buscarino A, Fortuna CFL, Frasca M (2016) Passive and active vibrations allow self-organization in large-scale electromechanical systems. Int J Bifurcat Chaos 26(07):1650123

    Article  Google Scholar 

  35. Bucolo M, Buscarino A, Famoso C et al (2019) Control of imperfect dynamical systems. Nonlin Dyn 98(4):2989–2999

    Article  MATH  Google Scholar 

  36. Bucolo M, Buscarino A, Famoso C et al (2021) Imperfections in integrated devices allow the emergence of unexpected strange attractors in electronic circuits. IEEE Access 9:29573–29583

    Article  Google Scholar 

  37. Tao G, Kokotovic PV (1994) Adaptive control of plants with unknown dead-zones. IEEE Trans Autom Contr 39(1):59–68

    Article  MATH  Google Scholar 

  38. Wang XS, Su CY, Hong H (2004) Robust adaptive control of a class of nonlinear systems with unknown dead-zone. Automatica 40(3):407–413

    Article  MATH  Google Scholar 

  39. Zhou Q, Zhao S, Li H et al (2019) Adaptive Neural Network Tracking Control for Robotic Manipulators With dead-zone. IEEE Trans Neur Netw Learn Sys 30(12):3611–3620

    Article  Google Scholar 

  40. Wang S, Yu H, Yu J et al (2020) Neural-network-based adaptive funnel control for servo mechanisms with unknown dead-zone. IEEE Trans Cybern 50(4):1383–1394

    Article  Google Scholar 

  41. Yu J, Shi P, Dong W, Lin C (2018) Adaptive fuzzy control of nonlinear systems with unknown dead zones based on command filtering. IEEE Trans Fuzzy Sys 26(1):46–55

    Article  Google Scholar 

  42. Espitia N, Perruquetti W (2021) Predictor-feedback prescribed-time stabilization of LTI systems with input delay. IEEE Trans Autom Contr 67(6):2784–2799

    Article  MATH  Google Scholar 

  43. Zhou Y, Wang X, Xu R (2022) Command-filter-based adaptive neural tracking control for a class of nonlinear MIMO state-constrained systems with input delay and saturation. Neur Netw 147:152–162

    Article  Google Scholar 

  44. Zhang J, Li S, Ahn CK et al (2022) Decentralized event-triggered adaptive fuzzy control for nonlinear switched large-scale systems with input delay via command-filtered backstepping. IEEE Trans Fuzzy Sys 30(6):2118–2123

    Article  Google Scholar 

  45. Li H, Liu Q, Feng G et al (2021) Leader-follower consensus of nonlinear time-delay multiagent systems: A time-varying gain approach. Automatica 126:109444

    Article  MATH  Google Scholar 

  46. Li X, Li P (2021) Stability of time-delay systems with impulsive control involving stabilizing delays. Automatica 124:109336

    Article  MATH  Google Scholar 

  47. Liu G, Hua C, Liu PX et al (2021) Input-to-state stability for time-delay systems with large delays. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2021.3106793

    Article  Google Scholar 

  48. Sun J, Yang J, Zeng Z (2022) Predictor-based periodic event-triggered control for nonlinear uncertain systems with input delay. Automatica 136:110055

    Article  MATH  Google Scholar 

  49. Li H, Wang L, Du H et al (2017) Adaptive fuzzy backstepping tracking control for strict-feedback systems with input delay. IEEE Trans Fuzzy Sys 25(3):642–652

    Article  Google Scholar 

  50. Li D, Liu Y, Tong S et al (2019) Neural networks-based adaptive control for nonlinear state constrained systems with input delay. IEEE Trans Cybern 49(4):1249–1258

    Article  Google Scholar 

  51. Ma J, Xu S, Cui G et al (2019) Adaptive backstepping control for strict-feedback non-linear systems with input delay and disturbances. IET Contr Theory Appl 13(4):506–516

    Article  MATH  Google Scholar 

  52. Ma J, Xu S, Li Y et al (2018) Neural networks-based adaptive output feedback control for a class of uncertain nonlinear systems with input delay and disturbances. J Frankl Instit 355(13):5503–5519

    Article  MATH  Google Scholar 

  53. Zhang Q, Dong J (2020) Disturbance-observer-based adaptive fuzzy control for nonlinear state constrained systems with input saturation and input delay. Fuzzy Sets Sys 392:77–92

    Article  MATH  Google Scholar 

  54. Sun H, Li S, Yang J et al (2015) Global output regulation for strict-feedback nonlinear systems with mismatched nonvanishing disturbances. Int J Robust Nonlin Contr 25(15):2631–2645

    Article  MATH  Google Scholar 

  55. Sun Y, Xu J, Lin G et al (2021) Adaptive neural network control for maglev vehicle systems with time-varying mass and external disturbance. Neur Comput Appl. https://doi.org/10.1007/s00521-021-05874-2

    Article  Google Scholar 

  56. Sun Y, Xu J, Chen C et al (2022) Reinforcement learning-based optimal tracking control for levitation system of maglev vehicle with input time delay. IEEE Trans Instrument Measur 71:1–13

    Google Scholar 

  57. Wang D, Huang J (2005) Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form. IEEE Trans Neural Netw 16(1):195–202

    Article  Google Scholar 

  58. Wang M, Wang C, Shi P et al (2016) Dynamic learning from neural control for strict-feedback systems with guaranteed predefined performance. IEEE Trans Neur Netw Learn Sys 27(12):2564–2576

    Article  Google Scholar 

Download references

Acknowledgements

This research was financially supported by the National Natural Science Foundation of China (Grants Nos. 11871117 and 61873041).

Author information

Authors and Affiliations

  1. College of Mathetatical Science, Bohai University, Jinzhou, 121013, Liaoning, China

    Junchang Zhai, Huanqing Wang & Jiaqing Tao

Authors
  1. Junchang Zhai
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Huanqing Wang
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Jiaqing Tao
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Junchang Zhai.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor 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

Zhai, J., Wang, H. & Tao, J. Disturbance-observer-based adaptive dynamic surface control for nonlinear systems with input dead-zone and delay using neural networks. Neural Comput & Applic 35, 4027–4049 (2023). https://doi.org/10.1007/s00521-022-07865-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-022-07865-3

Keywords