Skip to main content
SpringerLink
Log in

Adaptive Neural Tracking Control of Full-state Constrained Nonstrict-feedback Time-delay Systems with Input Saturation

  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

In this study, an adaptive neural backstepping control scheme is proposed for a class of nonstrict-feedback time-delay systems with input saturation, full-state constraints and unknown disturbances. A structural property of radial basis function neural network is presented to deal with the design from the nonstrict-feedback formation. This method does not require the parameter separation technique and its assumption. With the help of the Lyapunov-Krasovskii functionals and Young’s inequalities, the effects of time delays are compensated, and the unknown disturbances are eliminated in the design process. The barrier Lyapunov function (BLF) is applied to arrest the violation of the full-state constraints. To overcome the problem of input saturation nonlinearity, the smooth nonaffme function of the control input signal is adopted to approach the input saturation function. Moreover, an adaptive backstepping neural control strategy is proposed. The proposed adaptive neural controller ensures that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB). Furthermore, the tracking error can converge to a small neighborhood of the origin. The simulation result shows the effectiveness of this method.

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

Similar content being viewed by others

References

  1. X. Zhao, X. Wang, L. Ma, and G. Zong, “Fuzzy-approximation-based asymptotic tracking control for a class of uncertain switched nonlinear systems,” IEEE Transactions on Fuzzy Systems, 2019. DOI: 10.1109/TFUZZ.2019.2912138

    Google Scholar 

  2. L. Ma, X. Huo, X. Zhao, B. Niu, and G. Zong, “Adaptive neural control for switched nonlinear systems with unknown backlash-like hysteresis and output dead-zone,” Neuro computing, vol. 357, no. 10, pp. 203–214, September 2019.

    Google Scholar 

  3. X. Xie, D. Yue, and C. Peng, “Relaxed real-time scheduling stabilization of discrete-time Takagi-Sugeno fuzzy systems via an alterable-weights-based ranking switching mechanism,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 6, pp. 3808–3819, December 2018.

    Google Scholar 

  4. X. Xie, D. Yue, and C. Peng, “Observer design of discrete-time fuzzy systems based on an alterable weights method,” IEEE Transactions on Cybernetics, 2018. DOI: 10.1109/TCYB.2018.2878419

    Google Scholar 

  5. W. Qi, G. Zong, and H. R. Karimi, “Sliding mode control for nonlinear stochastic singular semi-Markov jump systems,” IEEE Transactions on Automatic Control, vol. 65, no. 1, pp. 361–368, Jan. 2020.

    MathSciNet  MATH  Google Scholar 

  6. W. Qi, G. Zong, and H. R. Karimi, “Sliding mode control for nonlinear stochastic semi-Markov switching systems with application to space robot manipulator model,” IEEE Transactions on Industrial Electronics, 2019. DOI: 10.1109/TIE.2019.2920619

    Google Scholar 

  7. H. Wang, P. X. Liu, X. Zhao, and X. Liu, “Adaptive fuzzy finite-time control of nonlinear systems with actuator faults,” IEEE Transactions on Cybernetics, 2019. DOI: 10.1109/TCYB.2019.2902868

    Google Scholar 

  8. H. Wang, P. X. Liu, J. Bao, X. Xie, and S. Li, “Adaptive neural output-feedback decentralized control for large-scale nonlinear systems with stochastic disturbances,” IEEE Transactions on Neural Networks and Learning Systems, 2019. DOI: 10.1109/TNNLS.2019.2912082

    Google Scholar 

  9. H. Wang, P. X. Liu, X. Xie, X. Liu, T. Hayat, and F. E. Alsaadi, “Adaptive fuzzy asymptotical tracking control of nonlinear systems with unmodeled dynamics and quantized actuator,” Information Sciences, April 2018. DOI: 10.1016/j.ins.2018.04.011

    Google Scholar 

  10. Y. Li, K. Li, and S. Tong, “Adaptive neural network finite-time control for multi-input and multi-output nonlinear systems with positive powers of odd rational numbers,” IEEE Transactions on Neural Networks and Learning Systems, 2019. DOI: 10.1109/TNNLS.2019.2933409

    Google Scholar 

  11. S. Yoo, “Adaptive tracking control for uncertain switched nonlinear systems in nonstrict-feedback form,” Journal of the Franklin Institute, vol. 353, no. 6, pp. 1409–1422, April 2016.

    MathSciNet  MATH  Google Scholar 

  12. W. Lin and C. Qian, “Adaptive control of nonlinearly parameterized systems: the smooth feedback case,” IEEE Transactions on Automatic Control, vol. 47, no. 8, pp. 1249–1266, August 2002.

    MathSciNet  MATH  Google Scholar 

  13. Q. Zhou, L. Wang, C. Wu, H. Li, and H. Du, “Adaptive fuzzy control for nonstrict-feedback systems with input saturation and output constraint,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 1, pp. 1–12, January 2017.

    Google Scholar 

  14. S. Yoo, “Approximation-based adaptive tracking of a class of uncertain nonlinear time-delay systems in nonstrict-feedback form,” International Journal of Systems Science, vol. 48, no. 7, pp. 1347–1355, November 2016.

    MathSciNet  MATH  Google Scholar 

  15. X. Zhang, F. Wang, and L. Zhang, “Finite time controller design of nonlinear quantized systems with nonstrict feedback form,” International Journal of Control, Automation and Systems, vol. 17, no. 1, pp. 225–233, January 2019.

    Google Scholar 

  16. K. P. Tee, S. S. Ge, and E. H. Tay, “Barrier Lyapunov functions for the control of output-constrained nonlinear systems,” Automatica, vol. 45, no. 4, pp. 918–927, April 2009.

    MathSciNet  MATH  Google Scholar 

  17. K. P. Tee and S. S. Ge, “Control of nonlinear systems with partial state constraints using a barrier Lyapunov function,” International Journal of Control, vol. 84, no. 12, pp. 2008–2023, November 2011.

    MathSciNet  MATH  Google Scholar 

  18. B. Ren, S. S. Ge, K. P. Tee, and T. H. Lee, “Adaptive neural control for output feedback nonlinear systems using a barrier Lyapunov function,” IEEE Transactions on Neural Networks, vol. 21, no. 8, pp. 1339–1345, August 2010.

    Google Scholar 

  19. Y. Liu and S. Tong, “Barrier Lyapunov functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints,” Automatica, vol. 64, no. C, pp. 70–75, February 2016.

    Google Scholar 

  20. Y. Li, X. Min, and S. Tong, “Adaptive fuzzy inverse optimal control for uncertain nonlinear systems with full-state constraints,” IEEE Transactions on Fuzzy Systems, 2019. DOI: 10.1109/TFUZZ.2019.2935693

    Google Scholar 

  21. J. Zhang, “Integral barrier Lyapunov functions-based neural control for strict-feedback nonlinear systems with multi-constraint,” International Journal of Control, Automation and Systems, vol. 16, no. 4, pp. 2002–2010, August 2018.

    Google Scholar 

  22. W. Si, X. Dong, and F. Yang, “Adaptive neural tracking control for nonstrict-feedback stochastic nonlinear time-delay systems with full-state constraints,” International Journal of Systems Science, vol. 48, no. 14, pp. 3018–3031, August 2017.

    MathSciNet  MATH  Google Scholar 

  23. Y. Li, T. Li, and X. Jing, “Indirect adaptive fuzzy control for input and output constrained nonlinear systems using a barrier Lyapunov function,” International Journal of Adaptive Control and Signal Processing, vol. 28, no. 2, pp. 184–199, February 2014.

    MathSciNet  MATH  Google Scholar 

  24. C. Wang, Y. Wu, and J. Yu, “Barrier Lyapunov functions-based adaptive control for nonlinear pure-feedback systems with time-varying full state constraints,” International Journal of Control, Automation and Systems, vol. 15, no. 6, pp. 2714–2722, December 2017.

    Google Scholar 

  25. D. Li, D. Li, Y. Liu, S. Tong, and C. L. P. Chen, “Approximation-based adaptive neural tracking control of nonlinear MIMO unknown time-varying delay systems with full state constraints,” IEEE Transactions on Cybernetics, vol. 47, no. 10, pp. 3100–3109, October 2017.

    Google Scholar 

  26. R. Li, B. Niu, Z. Feng, J. Li, P. Duan, and D. Yang, “Adaptive neural design frame for uncertain stochastic nonlinear non-lower triangular pure-feedback systems with input constraint,” Journal of the Franklin Institute, vol. 356, no. 6, pp. 9545–9564, Nov. 2019.

    MathSciNet  MATH  Google Scholar 

  27. L. Ma, X. Huo, X. Zhao, and G. Zong, “Adaptive fuzzy tracking control for a class of uncertain switched nonlinear systems with multiple constraints: a small-gain approach,” International Journal of Fuzzy Systems, vol. 21, no. 8, pp. 2609–2624, Nov. 2019.

    MathSciNet  Google Scholar 

  28. S. Yang, Z. Sun, Z. Wang, and T. Li, “A new approach to global stabilization of high-order time-delay uncertain nonlinear systems via time-varying feedback and homogeneous domination,” Journal of the Franklin Institute, vol. 355, no. 14, pp. 6469–6492, September 2018.

    MathSciNet  MATH  Google Scholar 

  29. Z. Sun, Z. Song, T. Li, and S. Yang, “Output feedback stabilization for high-order uncertain feedforward time-delay nonlinear systems,” Journal of the Franklin Institute, vol. 352, no. 11, pp. 5308–5326, November 2015.

    MathSciNet  MATH  Google Scholar 

  30. X. Zhang and Y. Lin, “Adaptive output feedback control for a class of large-scale nonlinear time-delay systems,” Automatica, vol. 52, pp. 87–94, February 2015.

    MathSciNet  MATH  Google Scholar 

  31. C. Hua, L. Zhang, and X. Guan, “Reduced-order observer-based output feedback control of nonlinear time-delay systems with prescribed performance,” International Journal of Systems Science, vol. 47, no. 6, pp. 1384–1393, April 2016.

    MathSciNet  MATH  Google Scholar 

  32. X. Yan, X. Song, and X. Wang, “Global output-feedback stabilization for nonlinear time-delay systems with unknown control coefficients,” International Journal of Control, Automation and Systems, vol. 16, no. 4, pp. 1550–1557, August 2018.

    Google Scholar 

  33. C. Hua and X. Guan, “Smooth dynamic output feedback control for multiple time-delay systems with nonlinear uncertainties,” Automatica, vol. 68, pp. 1–8, June 2016.

    MathSciNet  MATH  Google Scholar 

  34. J. Li, Y. Zhao, Z. Feng, and M. Park, “Reachable set estimation and dissipativity for discrete-time T-S fuzzy singular systems with time-varying delays,” Nonlinear Analysis: Hybrid Systems, vol. 31, no. 9, pp. 166–179, February 2019.

    MathSciNet  MATH  Google Scholar 

  35. J. Li, Z. Feng, Y. Zhao, and J. Shi, “Reachable set estimation for discrete-time bilinear systems with time-varying delays,” Journal of the Franklin Institute, vol. 355, no. 13, pp. 5721–5735, September 2018.

    MathSciNet  MATH  Google Scholar 

  36. Y. Yang, J. Tan, and D. Yue, “Prescribed performance tracking control of a class of uncertain pure-feedback nonlinear systems with input saturation,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, January 2018. DOI: 10.1109/TSMC.2017.2784451

    Google Scholar 

  37. Y. Li, S. Tong, and T. Li, “Hybrid fuzzy adaptive output feedback control design for uncertain MIMO nonlinear systems with time-varying delays and input saturation,” IEEE Transactions on Fuzzy Systems, vol. 24, no. 4, pp. 841–853, August 2016.

    Google Scholar 

  38. S. Sui, S. Tong, and Y. Li, “Observer-based fuzzy adaptive prescribed performance tracking control for nonlinear stochastic systems with input saturation,” Neurocomputing, vol. 158, no. 22, pp. 100–108, June 2015.

    Google Scholar 

  39. W. He, Y. Dong, and C. Sun, “Adaptive neural impedance control of a robotic manipulator with input saturation,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 46, no. 3, pp. 334–344, March 2016.

    Google Scholar 

  40. J. Wang and J. Zhao, “On improving transient performance in tracking control for switched systems with input saturation via composite nonlinear feedback,” International Journal of Robust and Nonlinear Control, vol. 26, no. 3, pp. 509–518, February 2016.

    MathSciNet  MATH  Google Scholar 

  41. C. Hua, G. Liu, L. Zhang, and X. Guan, “Output feedback tracking control for nonlinear time-delay systems with tracking errors and input constraints,” Neurocomputing, vol. 173, part 3, no. 15, pp. 751–758, January 2016.

    Google Scholar 

  42. C. Wen, J. Zhou, Z. Liu, and H. Su, “Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance,” IEEE Transactions on Automatic Control, vol. 56, no. 7, pp. 1672–1678, July 2011.

    MathSciNet  MATH  Google Scholar 

  43. S. S. Ge and K. P. Tee, “Approximation-based control of nonlinear MIMO time-delay systems,” Automatica, vol. 43, no. 1, pp. 31–43, January 2007.

    MathSciNet  MATH  Google Scholar 

  44. Y. Sun, B. Chen, C. Lin, H. Wang, and S. Zhou, “Adaptive neural control for a class of stochastic nonlinear systems by backstepping approach,” Information Sciences, vol. 369, no. 10, pp. 748–764, November 2016.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electronic and Information Engineering, University of Science and Technology Liaoning, Anshan, Liaoning, 114051, P. R. China

    Xin Liu, Chuang Gao & Yonghui Yang

  2. School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan, Shandong, 250101, P. R. China

    Huanqing Wang

  3. School of Sciences, University of Science and Technology Liaoning, Anshan, Liaoning, 114051, P. R. China

    Libing Wu

Authors
  1. Xin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chuang Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Huanqing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Libing Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yonghui Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yonghui Yang.

Additional information

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

Recommended by Associate Editor Xiangpeng Xie under the direction of Editor PooGyeon Park. This work is supported in part by the Taishan Scholar Project of Shandong Province of China under Grant tsqn201812093.

Xin Liu received his B.Sc. degree in Electrical Engineering and Automation from University of Science and Technology Liaoning, Anshan, China, in 2015. He is currently pursuing an M.S. degree in Control Engineering with University of Science and Technology Liaoning, Anshan, China. His research interests include fuzzy control, adaptive control, and control of nonlinear time-delay systems.

Chuang Gao received his B.S. and M.S. degrees from Warwick University and King’s College London, UK, in 2005 and 2007, respectively. He is currently a Ph.D. candidate in University of Science and Technology Liaoning, China. He has authored over 10 research papers indexed by SCI and EI. His research interests include nonlinear system control, machine learning and intelligent control.

Huanqing Wang received his B.Sc. degree in mathematics from Bohai University, Jinzhou, China, in 2003, an M.Sc. degree in mathematics from Inner Mongolia University, Huhhot, China, in 2006, and a Ph.D. degree from the Institute of Complexity Science, Qingdao University, Qingdao, China, in 2013. He was a Post-Doctoral Fellow with the Department of Electrical Engineering, Lakehead University, Thunder Bay, ON Canada, in 2014, and was a Post- Doctoral Fellow with the Department of Systems and Computer Engineering, Carleton University, Ottawa, ON Canada. He has authored or co-authored over 50 papers in top international journals. His current research interests include adaptive backstepping control, fuzzy control, neural networks control, stochastic nonlinear systems. Dr. Wang serves as an Associate Editor for several journals, including Neural Computing and Applications, the International Journal of Control, Automation, and Systems, and the IEEE ACCESS.

Libing Wu received his B.S. and M.S. degrees in the Department of Mathematics from Jinzhou Normal College, Jinzhou, China, in 2004, and in Basic Mathematics from Northeastern University, Shenyang, China, in 2007, respectively, and a Ph.D. degree in Control Theory and Control Engineering from Northeastern University, Shenyang, China, in 2016. He is currently an Associate Professor at the School of Science, University of Science and Technology Liaoning, and also as a Postdoctoral Fellow at the Department of Electrical Engineering, Yeungnam University. His research interests include adaptive control, fault-tolerant control, nonlinear control and fault estimation.

Yonghui Yang received his B.Sc. degree in Computer Science, from Northeastern University, Shenyang, China, an M.Sc. degree in Electronic and Information Engineering and a Ph.D. degree in Chemical Engineering from University of Science and Technology Liaoning, Anshan, China, in 1995, 2010, and 2018, respectively. He is currently a Professor at the School of Electronic and Information Engineering, University of Science and Technology Liaoning, Anshan, China. His research interests include nonlinear control, intelligent process control, robot communication and control, and machine learning.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, X., Gao, C., Wang, H. et al. Adaptive Neural Tracking Control of Full-state Constrained Nonstrict-feedback Time-delay Systems with Input Saturation. Int. J. Control Autom. Syst. 18, 2048–2060 (2020). https://doi.org/10.1007/s12555-019-0479-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-019-0479-5

Keywords

Search

Navigation