Skip to main content
SpringerLink
Log in

Observer-Based Adaptive NN Tracking Control for Nonstrict-Feedback Systems with Input Saturation

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

Input saturation is one of the common phenomena in many practical systems, and it is main obstacles that limits the systems performance. In this paper, the adaptive neural network (NN) control problem has been discussed for a family of uncertain nonstrict-feedback systems with input saturation. The innovations are summarized as follows: (1) the auxiliary systems and the NN state observer are developed to eliminate the influence of input saturation and estimate unmeasurable states; (2) in order to against the drawback of “explosion of complexity" for the traditional backstepping control technique (BCT), the dynamic surface control technique is used to reduce the excessive computation burden; (3) the proposed NN control approach for nonstrict-feedback systems only utilize the property of radial basis function-neural networks (RBF-NNs), instead of the restrictive assumption. Furthermore, unknown smooth functions are approximated by RBF-NNs in nonlinear systems. By employing the BCT, an adaptive output-feedback controller has been constructed. Meanwhile, all signals in closed-loop system are semi-globally uniformly ultimate bounded. An explicit function with the saturation error and designed parameters is obtained, which indicates the tracking error can be tuned through the saturation error and designed parameters. Finally, the superiority of the proposed control technique is validated by two examples.

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
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Cao P, Yang Z, Sun L, Liang Y, Yang M, Guan R (2019) Image captioning with bidirectional semantic attention-based guiding of long short-term memory. Neural Process Lett 50(1):103–119

    Google Scholar 

  2. Singh AK, Pal BC (2018) Decentralized nonlinear control for power systems using normal forms and detailed models. IEEE Trans Power Syst 33(2):1160–1172

    Google Scholar 

  3. Wang T, Gao H, Qiu J (2016) A combined fault-tolerant and predictive control for network-based industrial processes. IEEE Trans Ind Electron 63(4):2529–2536

    Google Scholar 

  4. Chen CLP, Ren C, Du T (2016) Fuzzy observed-based adaptive consensus tracking control for second-order multiagent systems with heterogeneous nonlinear dynamics. IEEE Trans Fuzzy Syst 24(4):906–915

    Google Scholar 

  5. Niu B, Li H, Qin T, Karimi HR (2018) Adaptive NN dynamic surface controller design for nonlinear pure-feedback switched systems with time-delays and quantized input. IEEE Trans Syst Man Cybern Syst 48(10):1676–1688

    Google Scholar 

  6. Zhou Q, Li H, Wu C, Wang L, Ahn CK (2017) Adaptive fuzzy control of nonlinear systems with unmodeled dynamics and input saturation using small-gain approach. IEEE Trans Syst Man Cybern Syst 47(8):1979–1989

    Google Scholar 

  7. Yu J, Shi P, Lin C, Yu H (2020) Adaptive neural command filtering control for nonlinear MIMO systems with saturation input and unknown control direction. IEEE Trans Cybern 50(6):2536–2545

    Google Scholar 

  8. Li Y, Tong S (2017) Adaptive fuzzy output-feedback stabilization control for a class of switched nonstrict-feedback nonlinear systems. IEEE Trans Cybern 47(4):1007–1016

    Google Scholar 

  9. Tong S, Li Y, Liu Y (2021) Observer-based adaptive neural networks control for large-scale interconnected systems with nonconstant control gains. IEEE Trans Neural Netw Learn Syst 32(4):1575–1585

    MathSciNet  Google Scholar 

  10. 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

    Google Scholar 

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

    Article  Google Scholar 

  12. Pan Y, Du P, Xue H, Lam H (2020) Singularity-free fixed-time fuzzy control for robotic systems with user-defined performance. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2020.2999746

    Article  Google Scholar 

  13. Liang H, Liu G, Zhang H, Huang T (2020) Neural-network-based event-triggered adaptive control of nonaffine nonlinear multiagent systems with dynamic uncertainties. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.3003950

    Article  Google Scholar 

  14. Kanellakopoulos I, Kokotovic PV, Morse AS (1991) Systematic design of adaptive controllers for feedback linearizable systems. In: ACC 1991, IEEE, pp 649–654

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

    Google Scholar 

  16. Jia Y (2003) Alternative proofs for improved LMI representations for the analysis and the design of continuous-time systems with polytopic type uncertainty: a predictive approach. IEEE Trans Autom Control 48(8):1413–1416

    MathSciNet  MATH  Google Scholar 

  17. Xu C, Tong D, Chen Q, Zhou W (2020) Asynchronous control of T-S fuzzy chaotic systems via a unified model using the hidden Markov model subject to strict dissipativity. Optim Contr Appl Met 41(2):587–604

    MathSciNet  MATH  Google Scholar 

  18. Chen B, Liu X, Lin C (2018) Observer and adaptive fuzzy control design for nonlinear strict-feedback systems with unknown virtual control coefficients. IEEE Trans Fuzzy Syst 26(3):1732–1743

    Google Scholar 

  19. Xu C, Tong D, Chen Q, Zhou W, Shi P (2021) Exponential stability of Markovian jumping systems via adaptive sliding mode control. IEEE Trans Syst Man Cybern Syst 51(2):1249–1258

    Google Scholar 

  20. Liu Y, Guo BZ, Park JH, Lee S (2018) Event-based reliable dissipative filtering for T-S fuzzy systems with asynchronous constraints. IEEE Trans Fuzzy Syst 26(4):2089–2098

    Google Scholar 

  21. Xu Q, Li X (2020) HONN-based adaptive ILC for pure-feedback nonaffine discrete-time systems with unknown control directions. IEEE Trans Neural Netw Learn Syst 31(1):212–224

    MathSciNet  Google Scholar 

  22. Swaroop D, Hedrick JK, Yip PP, Gerdes JC (2000) Dynamic surface control for a class of nonlinear systems. IEEE Trans Autom Control 45(10):1893–1899

    MathSciNet  MATH  Google Scholar 

  23. Cui B, Xia Y, Liu K, Shen G (2020) Finite-time tracking control for a class of uncertain strict-feedback nonlinear systems with state constraints: A smooth control approach. IEEE Trans Neural Netw Learn Syst 31(11):4920–4932

    MathSciNet  Google Scholar 

  24. Tong S, Sui S, Li Y (2015) Fuzzy adaptive output feedback control of MIMO nonlinear systems with partial tracking errors constrained. IEEE Trans Fuzzy Syst 23(4):729–742

    Google Scholar 

  25. Li Y, Shao X, Tong S (2019) Adaptive fuzzy prescribed performance control of nontriangular structure nonlinear systems. IEEE Trans Cybern 28(10):2416–2426

    Google Scholar 

  26. Jia F, Wang X, Zhou X (2019) Robust adaptive prescribed performance control for a class of nonlinear pure-feedback systems. Int J Robust Nonlinear Control 29(12):3971–3987

    MathSciNet  MATH  Google Scholar 

  27. Li Y, Sun K, Tong S (2019) Observer-based adaptive fuzzy fault-tolerant optimal control for SISO nonlinear systems. IEEE Trans Cybern 49(2):649–661

    Google Scholar 

  28. Lu D, Tong D, Chen Q, Zhou W, Zhou J, Shen S (2021) Exponential synchronization of stochastic neural networks with time-varying delays and Lévy noises via event-triggered control. Neural Process Lett. https://doi.org/10.1007/s11063.021.10509.7

    Article  Google Scholar 

  29. Tong Y, Tong D, Chen Q, Zhou W (2020) Finite-time state estimation for nonlinear systems based on event-triggered mechanism. Circ Syst Signal Process 39(7):3737–3757

    MATH  Google Scholar 

  30. Wang M, Wang Z, Dong H, Han QL (2021) A novel framework for backstepping-based control of discrete-time strict-feedback nonlinear systems with multiplicative noises. IEEE Trans Autom Control 66(4):1484–1496

    MathSciNet  MATH  Google Scholar 

  31. Jia Y (2000) Robust control with decoupling performance for steering and traction of 4WS vehicles under velocity-varying motion. IEEE Trans Control Syst Technol 8(3):554–569

    Google Scholar 

  32. Chen Q, Tong D, Zhou W, Xu Y, Mou J (2021) Exponential stability using sliding mode control for stochastic neutral-type systems. Circ Syst Signal Process 40:2006–2024

    Google Scholar 

  33. Tong D, Xu C, Chen Q, Zhou W, Xu Y (2020) Sliding mode control for nonlinear stochastic systems with Markovian jumping parameters and mode-dependent time-varying delays. Nonlinear Dyn 100(2):1343–1358

    MATH  Google Scholar 

  34. Tong D, Rao P, Chen Q, Ogorzalek M, Li X (2018) Exponential synchronization and phase locking of a multilayer Kuramoto-oscillator system with a pacemaker. Neurocomputing 308:129–137

    Google Scholar 

  35. Tong S, Li Y, Sui S (2016) Adaptive fuzzy tracking control design for SISO uncertain nonstrict feedback nonlinear systems. IEEE Trans Fuzzy Syst 24(6):1441–1454

    Google Scholar 

  36. Wu C, Liu J, Xiong Y, Wu L (2018) Observer-based adaptive fault-tolerant tracking control of nonlinear nonstrict-feedback systems. IEEE Trans Neural Netw Learn Syst 29(7):3022–3033

    MathSciNet  Google Scholar 

  37. Pérez-Arancibia NO, Tsao TC, Gibson JS (2010) Saturation-induced instability and its avoidance in adaptive control of hard disk drives. IEEE Trans Control Syst Technol 18(2):368–382

    Google Scholar 

  38. Li Z, Li T, Feng G, Zhao R, Shan Q (2020) Neural network-based adaptive control for pure-feedback stochastic nonlinear systems with time-varying delays and dead-zone input. IEEE Trans Syst Man Cybern Syst 50(12):5317–5329

    Google Scholar 

  39. Wang L, Chen CP (2021) Reduced-order observer-based dynamic event-triggered adaptive NN control for stochastic nonlinear systems subject to unknown input saturation. IEEE Trans Neural Netw Learn Syst 32(4):1678–1690

    MathSciNet  Google Scholar 

  40. Li P, Yang G (2011) An adaptive fuzzy design for fault-tolerant control of mimo nonlinear uncertain systems. J Control Theory App 9(2):244–250

    MathSciNet  Google Scholar 

  41. Chen B, Lin C, Liu X, Liu K (2015) Adaptive fuzzy tracking control for a class of MIMO nonlinear systems in nonstrict-feedback form. IEEE Trans Cybern 45(12):2744–2755

    Google Scholar 

  42. Wang H, Liu X, Liu K, Karimi HR (2015) Approximation-based adaptive fuzzy tracking control for a class of nonstrict-feedback stochastic nonlinear time-delay systems. IEEE Trans Fuzzy Syst 23(5):1746–1760

    Google Scholar 

  43. Wang H, Chen B, Liu K, Liu X, Lin C (2014) Adaptive neural tracking control for a class of nonstrict-feedback stochastic nonlinear systems with unknown backlash-like hysteresis. IEEE Trans Neural Netw Learn Syst 25(5):947–958

    Google Scholar 

  44. Tong D, Xu C, Chen Q, Zhou W (2020) Sliding mode control of a class of nonlinear systems. J Franklin Inst 357(3):1560–1581

    MathSciNet  MATH  Google Scholar 

  45. Huang HC, Chiang CH (2016) An evolutionary radial basis function neural network with robust genetic-based immunecomputing for online tracking control of autonomous robots. Neural Process Lett 44(1):19–35

    Google Scholar 

  46. 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

    MathSciNet  Google Scholar 

  47. Keighobadi J, Hosseini-Pishrobat M, Faraji J (2020) Adaptive neural dynamic surface control of mechanical systems using integral terminal sliding mode. Neurocomputing 379:141–151

    Google Scholar 

  48. Tong D, Zhang L, Zhou W, Zhou J, Xu Y (2016) Asymptotical synchronization for delayed stochastic neural networks with uncertainty via adaptive control. Int J Control Autom 14(3):706–712

    Google Scholar 

  49. Wang J, Tian L (2019) Stability of inertial neural network with time-varying delays via sampled-data control. Neural Process Lett 50(2):1123–1138

    MathSciNet  Google Scholar 

  50. Liu Z, Lai G, Zhang Y, Chen CLP (2015) Adaptive neural output feedback control of output-constrained nonlinear systems with unknown output nonlinearity. IEEE Trans Neural Netw Learn Syst 26(8):1789–1802

    MathSciNet  Google Scholar 

  51. Yao B, Tomizuka M (1997) Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form. Automatica 33(5):893–900

    MathSciNet  MATH  Google Scholar 

  52. Zhou Q, Li H, Wang L, Lu R (2018) Prescribed performance observer-based adaptive fuzzy control for nonstrict-feedback stochastic nonlinear systems. IEEE Trans Syst Man Cybern Syst 48(10):1747–1758

    Google Scholar 

  53. Li Y, Yang G (2016) Fuzzy adaptive output feedback fault-tolerant tracking control of a class of uncertain nonlinear systems with nonaffine nonlinear faults. IEEE Trans Fuzzy Syst 24(1):223–234

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201620, China

    Xiang Liu, Dongbing Tong & Qiaoyu Chen

  2. College of Information Sciences and Technology, Donghua University, Shanghai, 201620, China

    Wuneng Zhou & Kaili Liao

Authors
  1. Xiang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dongbing Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qiaoyu Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wuneng Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Kaili Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Dongbing Tong or Qiaoyu Chen.

Additional information

Publisher's Note

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

This work is partially supported by National Natural Science Foundation of China (61673257), the Natural Science Foundation of Shanghai (20ZR1422400), the China Postdoctoral Science Foundation (2019M661322).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, X., Tong, D., Chen, Q. et al. Observer-Based Adaptive NN Tracking Control for Nonstrict-Feedback Systems with Input Saturation. Neural Process Lett 53, 3757–3781 (2021). https://doi.org/10.1007/s11063-021-10575-x

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-021-10575-x

Keywords

Search

Navigation