Skip to main content
Log in

Efficient learning control of uncertain nonlinear systems with input constraints: a disturbance observer-based neural network approach

  • Published:
International Journal of Dynamics and Control Aims and scope Submit manuscript

Abstract

To deal with the effects of the input saturation and time-varying input delay, this article presents a serial-parallel identifier-based composite neural network learning control for uncertain nonlinear systems subject to external disturbances. Based on the backstepping technique, a radial basis function network is adopted to identify the unknown term, where the neural network learning accuracy is studied by considering a modeling error. In addition, a compensation system is designed to cope with input delay and input saturation, simultaneously. Besides, the explosion of complexity is mitigated by employing the command-filtered control approach. To enhance the robust performance of the overall system, the proposed control structure is enriched by a disturbance observer. Therefore, new adaptive rules are constructed. The stability of the closed-loop system is ensured by the Lyapunov theorem. Simulation results clarify the efficiency of the proposed control algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data availablity

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

References

  1. Wang T, Zhang Y, Qiu J, Gao G (2015) Adaptive fuzzy backstepping control for a class of nonlinear systems with sampled and delayed measurements. IEEE Trans Fuzzy Syst 23(2):302–312

    Article  Google Scholar 

  2. Yao D, Dou C, Yue D, Zhao N, Zhang T (2020) Adaptive neural network consensus tracking control for uncertain multi-agent systems with predefined accuracy. Nonlinear Dyn 101(4):2249–2262

    Article  Google Scholar 

  3. Aslmostafa E, Ghaemi S, Badamchizadeh MA, Ghiasi AR (2022) Adaptive backstepping quantized control for a class of unknown nonlinear systems. ISA Trans 125:146–155

    Article  Google Scholar 

  4. Ma L, Huo X, Zhao X, Niu B, Zong G (2019) Adaptive neural control for switched nonlinear systems with unknown backlash-like hysteresis and output dead-zone. Neurocomputing 357:203–214

    Article  Google Scholar 

  5. Zheng S, Shi P, Wang S, Shi Y (2021) Adaptive neural control for a class of nonlinear multiagent systems. IEEE Trans Neural Netw Learn Syst 32(2):763–776

    Article  MathSciNet  Google Scholar 

  6. Lv W, Wang F, Li Y (2018) Finite-time adaptive fuzzy output-feedback control of MIMO nonlinear systems with hysteresis. Neurocomputing 296:74–81

    Article  Google Scholar 

  7. Du P, Zhou Q, Liang H (2020) Neural adaptive prescribed performance control for interconnected nonlinear systems with output dead zone. Int J Robust Nonlinear Control 30(3):999–1020

    Article  MathSciNet  Google Scholar 

  8. Wang W, Tong S (2018) Adaptive fuzzy bounded control for consensus of multiple strict-feedback nonlinear systems. IEEE Trans Cyber 48(2):522–531

    Article  MathSciNet  Google Scholar 

  9. Saadat SA, Fateh MM, Keighobadi J (2022) Adaptive state augmented clustering-based fuzzy learning control of a passive torque simulator. Int J Dyn Control 10:917–929

    Article  MathSciNet  Google Scholar 

  10. Liu J (2014) Observer-based backstepping dynamic surface control for stochastic nonlinear strict-feedback systems. Neural Comput Appl 24(5):1067–1077

    Article  Google Scholar 

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

    Article  Google Scholar 

  12. Zhou Z, Tong D, Chen Q, Zhou W, Xu Y (2021) Adaptive NN control for nonlinear systems with uncertainty based on dynamic surface control. Neurocomputing 421:161–172

    Article  Google Scholar 

  13. Sun W, Su SF, Xia J, Zhuang G (2021) Command filter-based adaptive prescribed performance tracking control for stochastic uncertain nonlinear systems. IEEE Trans Syst Man Cybern Syst 51(10):6555–6563

    Article  Google Scholar 

  14. Soukkou Y, Soukkou A, Tadjine M, Nibouche M, Haddad S, Benghanem M (2023) Robust adaptive finite time command filtered backstepping control for uncertain output constrained strict-feedback nonlinear systems. Int J Dyn Control. https://doi.org/10.1007/s40435-023-01255-w

    Article  Google Scholar 

  15. Hu Y, Liu W (2023) Adaptive fuzzy dynamic surface control for nonstrict-feedback nonlinear state constrained systems with input dead-zone via event-triggered sampling. Appl Math Comput 450:127985

    MathSciNet  Google Scholar 

  16. Pan Y, Zhou Y, Sun T, Er MJ (2013) Composite adaptive fuzzy H\(_\infty \) tracking control of uncertain nonlinear systems. Neurocomputing 99:15–24

    Article  Google Scholar 

  17. Pahnehkolaei SMA, Keighobadi J, Alfi A, Modares H (2021) Compound FAT-based learning control of uncertain fractional-order nonlinear systems with disturbance. IEEE Control Syst Lett 6:1519–1524

    Article  MathSciNet  Google Scholar 

  18. Pan Y, Yang C, Pratama M, Yu H (2019) Composite learning adaptive backstepping control using neural networks with compact supports. Int J Adapt Control Signal Process 33(12):1726–1738

    Article  MathSciNet  Google Scholar 

  19. Xu B, Zhang R, Li S, He W, Shi Z (2020) Composite neural learning-based nonsingular terminal sliding mode control of MEMS gyroscopes. IEEE Trans Neural Netw Learn Syst 31(4):1375–1386

    Article  MathSciNet  Google Scholar 

  20. Keighobadi J, Xu B, Alfi A, Arabkoohsar A, Nazmara G (2022) Compound FAT-based prespecified performance learning control of robotic manipulators with actuator dynamics. ISA Trans 131:246–263

    Article  Google Scholar 

  21. Aghayan ZS, Alfi A, Machado JT (2022) Guaranteed cost-based feedback control design for fractional-order neutral systems with input-delayed and nonlinear perturbations. ISA Trans 131:95–107

    Article  Google Scholar 

  22. Zhou Q, Wu C, Jing X, Wang L (2016) Adaptive fuzzy backstepping dynamic surface control for nonlinear input-delay systems. Neurocomputing 199:58–65

    Article  Google Scholar 

  23. Niu B, Li L (2018) Adaptive backstepping-based neural tracking control for MIMO nonlinear switched systems subject to input delays. IEEE Trans Neural Netw Learn Syst 29(6):2638–2644

    Article  MathSciNet  Google Scholar 

  24. Keighobadi J, Fateh MM, Xu B (2020) Adaptive fuzzy voltage-based backstepping tracking control for uncertain robotic manipulators subject to partial state constraints and input delay. Nonlinear Dyn 100:2609–2634

    Article  Google Scholar 

  25. Li Y, Qu F, Tong S (2021) Observer-based fuzzy adaptive finite-time containment control of nonlinear multiagent systems with input delay. IEEE Trans Cybern 51(1):126–137

    Article  Google Scholar 

  26. Zirkohi MM (2022) Robust adaptive backstepping control of uncertain fractional-order nonlinear systems with input time delay. Math Comput Simul 196:251–272

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  28. Li DP, Liu YJ, Tong S, Chen CP, Li DJ (2019) Neural networks-based adaptive control for nonlinear state constrained systems with input delay. IEEE Trans Cybern 49(4):1249–1258

    Article  Google Scholar 

  29. Deng W, Yao J, Ma D (2018) Time-varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach. Int J Robust Nonlinear Control 28(1):31–52

    Article  MathSciNet  Google Scholar 

  30. Liu Y, Li M (2015) Improved robust stabilization method for linear systems with interval time-varying input delays by using wirtinger inequality. ISA Trans 56:111–122

    Article  Google Scholar 

  31. Fan X, Yu K (2020) Adaptive fuzzy dynamic surface control for nonlinear systems with time-varying input delay and sampled data. Int J Fuzzy Syst 22(7):2236–2245

    Article  Google Scholar 

  32. Wang S, Wang W, Xiong S (2016) Impact angle constrained three-dimensional integrated guidance and control for STT missile in the presence of input saturation. ISA Trans 64:151–160

    Article  Google Scholar 

  33. Li Y, Tong S, Li T (2016) Hybrid fuzzy adaptive output feedback control design for uncertain MIMO nonlinear systems with time-varying delays and input saturation. IEEE Trans Fuzzy Syst 24(4):841–853

    Article  Google Scholar 

  34. Zhou X, Gao C, Li ZG, Ouyang XG, Wu LG (2021) Observer-based adaptive fuzzy finite-time prescribed performance tracking control for strict-feedback systems with input dead-zone and saturation. Nonlinear Dyn 103(2):1645–1661

    Article  Google Scholar 

  35. Gao YF, Sun XM, Wen C, Wang W (2017) Adaptive tracking control for a class of stochastic uncertain nonlinear systems with input saturation. IEEE Trans Autom Control 62(5):2498–2504

    Article  MathSciNet  Google Scholar 

  36. 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 Neural Netw Learn Syst 26(9):2086–2097

    Article  MathSciNet  Google Scholar 

  37. Chang W, Tong S, Li Y (2017) Adaptive fuzzy backstepping output constraint control of flexible manipulator with actuator saturation. Neural Comput Appl 28(1):1165–1175

    Article  Google Scholar 

  38. Peydayesh A, Arefi MM, Modares H (2018) Distributed neuro-adaptive control protocols for non-strict feedback non-linear MASs with input saturation. IET Control Theory Appl 12(11):1611–1620

    Article  MathSciNet  Google Scholar 

  39. Wang P, Zhang X, Zhu J (2019) Online performance-based adaptive fuzzy dynamic surface control for nonlinear uncertain systems under input saturation. IEEE Trans Fuzzy Syst 27(2):209–220

    Article  Google Scholar 

  40. Sun K, Qiu J, Karimi HR, Gao H (2021) A novel finite-time control for nonstrict feedback saturated nonlinear systems with tracking error constraint. IEEE Trans Syst Man Cybernet Syst 51(6):3968–3979

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  42. Li YD, Chen B (2021) Adaptive neural tracking control for a class of nonlinear systems with input delay and saturation. Syst Sci Control Eng 9(sup2):21–28

    Article  Google Scholar 

  43. Li YD, Chen B, Lin C, Shang Y (2021) Adaptive neural decentralized output-feedback control for nonlinear large-scale systems with input time-varying delay and saturation. Neurocomputing 427:212–224

    Article  Google Scholar 

  44. 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. Neural Netw 147:152–162

    Article  Google Scholar 

  45. Chen WH (2004) Disturbance observer based control for nonlinear systems. IEEE/ASME Trans Mechatron 9(4):706–710

    Article  Google Scholar 

  46. Chen WH, Yang J, Guo L, Li S (2016) Disturbance-observer-based control and related methods-an overview. IEEE Trans Industr Electron 63(2):1083–1095

    Article  Google Scholar 

  47. Mehrjouyan A, Menhaj MB, Khosravi MA (2021) Robust observer-based adaptive synchronization control of uncertain nonlinear bilateral teleoperation systems under time-varying delay. Measurement 182:109542

    Article  Google Scholar 

  48. Chen B, Feng Y, Cao Y (2023) Backstepping control based on disturbance observer and equilibrium manifold linearization model for power-line inspection robots. Int J Dyn Control 11:3124–3135

    Article  MathSciNet  Google Scholar 

  49. Zhang JJ (2019) State observer-based adaptive neural dynamic surface control for a class of uncertain nonlinear systems with input saturation using disturbance observer. Neural Comput Appl 31(9):4993–5004

    Article  Google Scholar 

  50. He W, Sun Y, Yan Z, Yang C, Li Z, Kaynak O (2020) Disturbance observer-based neural network control of cooperative multiple manipulators with input saturation. IEEE Trans Neural Netw Learn Syst 31(5):1735–1746

    Article  MathSciNet  Google Scholar 

  51. Han SI (2019) Fuzzy supertwisting dynamic surface control for MIMO strict-feedback nonlinear dynamic systems with supertwisting nonlinear disturbance observer and a new partial tracking error constraint. IEEE Trans Fuzzy Syst 27(11):2101–2114

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  53. Zhai J, Wang H, Tao J (2023) Disturbance-observer-based adaptive dynamic surface control for nonlinear systems with input dead-zone and delay using neural networks. Neural Comput Appl 35(5):4027–4049

    Article  Google Scholar 

  54. Xu B, Sun F, Pan Y, Chen B (2017) Disturbance observer based composite learning fuzzy control of nonlinear systems with unknown dead zone. IEEE Trans Syst Man Cybern Syst 47(8):1854–1862

  55. Xu B, Sun F (2018) Composite intelligent learning control of strict-feedback systems with disturbance. IEEE Trans Cybern 48(2):730–741

  56. Deng H, Krstić M (1997) Stochastic nonlinear stabilizationI: a backstepping design. Syst Control Lett 32(3):143–150

  57. Li Y, Tong S, Li T (2015) Composite adaptive fuzzy output feedback control design for uncertain nonlinear strict-feedback systems with input saturation. IEEE Trans Cybern 45(10):2299–2308

    Article  Google Scholar 

  58. Wang LX (1995) Design and analysis of fuzzy identifiers of nonlinear dynamic systems. IEEE Trans Autom Control 40(1):11–23

    Article  MathSciNet  Google Scholar 

Download references

Funding

There is no funding.

Author information

Authors and Affiliations

Authors

Contributions

Javad Keighobadi:Problem formulation; Control design; Writing-original draft; Writing-revised manuscript Ali Mehrjouyan: Data analysis; Software; Updating Software; Validation Alireza Alfi: Conceptualization; Writing-original draft; Writing- revised manuscript; Validation

Corresponding author

Correspondence to Javad Keighobadi.

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

Keighobadi, J., Mehrjouyan, A. & Alfi, A. Efficient learning control of uncertain nonlinear systems with input constraints: a disturbance observer-based neural network approach. Int. J. Dynam. Control (2024). https://doi.org/10.1007/s40435-024-01416-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40435-024-01416-5

Keywords

Navigation