Log in

Fixed-time Fuzzy Adaptive Decentralized Control for High-order Nonlinear Large-scale Systems

  • Regular Papers
  • Intelligent Control and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper studies a fuzzy adaptive fixed-time tracking control issue for nonlinear high-order largescale systems. Fuzzy logic systems (FLSs) are utilized to identify unknown nonlinearities. Through using adaptive backstep** and adding a power integrator technique, the fixed-time decentralized control method is presented. It is proved that the tracking errors converge to a small neighborhood of a fixed time. A simulation example is presented to confirm the validity of the developed control method.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /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 includes VAT (Canada)

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. H. Ma, H. J. Liang, H. J. Ma, and Q. Zhou, “Nussbaum gain adaptive backstep** control of nonlinear strict-feedback systems with unmodeled dynamics and unknown dead zone,” International Journal of Robust and Nonlinear Control, vol. 28, no. 17, pp. 5326–5343, 2018.

    MathSciNet  MATH  Google Scholar 

  2. F. Wang, Q. Zou, and Q. Zong, “Robust adaptive backstep** control for an uncertain nonlinear system with input constraint based on Lyapunov redesign,” International Journal of Control, Automation, and Systems, vol. 15, pp. 212–225, 2017.

    Google Scholar 

  3. J. P. Cai, C. Y. Wen, and H. Y. Su, “Adaptive backstep** control for a class of nonlinear systems with non-triangular structural uncertainties,” IEEE Transactions on Automatic Control, vol. 62, no. 10, pp. 5220–5226, 2017.

    MathSciNet  MATH  Google Scholar 

  4. C. C. Hua, X. P. Guan, and P. Shi, “Robust backstep** control for a class of time delayed systems,” IEEE Transactions on Automatic Control, vol. 50, no. 6, pp. 894–899, 2005.

    MathSciNet  MATH  Google Scholar 

  5. M. L. Chiang and L. C. Fu, “Adaptive stabilization of a class of uncertain switched nonlinear systems with backstep** control,” Automatica, vol. 50, no.8, pp. 2128–2135, 2014.

    MathSciNet  MATH  Google Scholar 

  6. C. C. Hua, P. X. Liu, and X. P. Guan, “Backstep** control for nonlinear systems with time delays and applications to chemical reactor systems,” IEEE Transactions on Industrial Electronics, vol. 56, no. 9, pp. 3723–3732, 2009.

    Google Scholar 

  7. R. H. Cui and X. J. **e, “Adaptive state-feedback stabilization of state-constrained stochastic high-order nonlinear systems,” Science China Information Sciences, vol. 64, Article number 200203, 2021.

    MathSciNet  Google Scholar 

  8. J. M. Peng, C. Y. Li, and X. D. Ye, “Cooperative control of high-order nonlinear systems with unknown control directions,” Systems and Control Letters, vol. 113, pp. 101–108, 2018.

    MathSciNet  MATH  Google Scholar 

  9. J. Davila, “Exact tracking using backstep** control design and high-order sliding modes,” IEEE Transactions on Automatic Control, vol. 58, no. 8, pp. 2077–2081, 2013.

    MathSciNet  MATH  Google Scholar 

  10. M. Chen, C. S. Jiang, and Q. X. Wu, “Backstep** control for a class of uncertain nonlinear systems with neural network,” International Journal of Nonlinear Science, vol. 3, no. 2, pp. 137–143, 2007.

    MathSciNet  MATH  Google Scholar 

  11. Y. H. Li, S. Qiang, and X. Y. Zhuang, “Robust and adaptive backstep** control for nonlinear systems using RBF neural networks,” IEEE Transactions on Neural Networks, vol. 15, no. 3, pp. 693–701, 2004.

    Google Scholar 

  12. Y. M. Li, S. C. Tong, and T. S. Li, “Adaptive fuzzy backstep** control design for a class of pure-feedback switched nonlinear systems,” Nonlinear Analysis: Hybrid Systems, vol. 16, pp. 72–80, 2015.

    MathSciNet  MATH  Google Scholar 

  13. S. C. Tong, Y. M. Li, G. Feng, and T. S. Li, “Observerbased adaptive fuzzy backstep** dynamic surface control for a class of MIMO nonlinear systems,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 41, no. 4, pp. 1124–1135, 2011.

    Google Scholar 

  14. S. C. Tong, S. Sui, and Y. M. Li, “Fuzzy adaptive output feedback control of MIMO nonlinear systems with partial tracking errors constrained,” IEEE Transactions on Fuzzy Systems, vol. 23, no. 4, pp. 729–742, 2015.

    Google Scholar 

  15. X. Zhang and Y. Lin, “Nonlinear decentralized control of large-scale systems with strong interconnections,” Automatica, vol. 50, no. 9, pp. 2419–2423, 2014.

    MathSciNet  MATH  Google Scholar 

  16. Y. M. Li, K. K. Sun, and S. C. Tong, “Adaptive fuzzy robust fault-tolerant optimal control for nonlinear large-scale systems,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 5, pp. 2899–2914, 2018.

    Google Scholar 

  17. S. C. Tong, Y. M. Li, and L. Y. Jun, “Adaptive fuzzy output feedback decentralized control of pure-feedback nonlinear large-scale systems,” International Journal of Robust and Nonlinear Control, vol. 24, no. 5, pp. 930–954, 2012.

    MathSciNet  MATH  Google Scholar 

  18. Y. M. Li and S. C. Tong, “Fuzzy adaptive control design strategy of nonlinear switched large-scale systems,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 48, no. 12, pp. 2209–2218, 2018.

    Google Scholar 

  19. Y. M. Li, Z. Y. Ma, and S. C. Tong, “Adaptive fuzzy outputconstrained fault-tolerant control of nonlinear stochastic large-scale systems with actuator faults,” IEEE Transactions on Cybernetics, vol. 47, no. 9, pp. 2362–2376, 2017.

    Google Scholar 

  20. K. W. Li, Y. M. Li, and G. D. Zong, “Adaptive fuzzy fixed-time decentralized control for stochastic nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 29, no. 11, pp. 3428–3440, 2021.

    Google Scholar 

  21. C. C. Hua, X. P. Guan, and P. Shi, “Adaptive fuzzy control for uncertain interconnected time-delay systems,” Fuzzy Sets and Systems, vol. 153, no. 3, pp. 447–458, 2005.

    MathSciNet  MATH  Google Scholar 

  22. S. J. Yoo and J. B. Park, “Neural-network-based decentralized adaptive control for a class of large-scale nonlinear systems with unknown timevarying delays,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 39, no. 5, pp. 1316–1323, 2009.

    Google Scholar 

  23. H. Q. Wang, B. Chen, and C. Lin, “Adaptive fuzzy decentralized control for a class of large-scale stochastic nonlinear systems,” Neurocomputing, vol. 103, pp. 155–163, 2013.

    Google Scholar 

  24. B. Wu, X. H. Chang, and X. D. Zhao, “Fuzzy H output feedback control for nonlinear NCSs with quantization and stochastic communication protocol,” IEEE Transactions on Fuzzy Systems, vol. 29, no. 9, pp. 2623–2634, 2021.

    Google Scholar 

  25. X. H. Chang, Q. Liu, Y. M. Wang, and J. **ong, “Fuzzy peak-to-peak filtering for networked nonlinear systems with multipath data packet dropouts,” IEEE Transactions on Fuzzy Systems, vol. 27, no. 3, pp. 436–446, 2019.

    Google Scholar 

  26. H. Wang and Q. X. Zhu, “Finite-time stabilization of high-order stochastic nonlinear systems in strict-feedback form,” Automatica, vol. 54, pp. 284–291, 2015.

    MathSciNet  MATH  Google Scholar 

  27. Y. L. Fan and Y. M. Li, “Adaptive fuzzy finite-time optimal control for switched nonlinear systems,” Optimal Control Applications and Methods, vol. 41, no. 5, pp. 1616–1631, 2020.

    MathSciNet  MATH  Google Scholar 

  28. L. Chu, T. Gao, M. X. Wang, Y. Q. Han, and S. L. Zhu, “Adaptive decentralized control for large-scale nonlinear systems with finite-time output constraints by multidimensional Taylor network,” Asian Journal of Control, vol. 24, no. 4, pp. 1769–1779, 2022.

    MathSciNet  Google Scholar 

  29. L. Y. Hu and X. H. Li, “Decentralised adaptive neural connectively finitetime control for a class of p-normal form largescale nonlinear systems,” International Journal of Systems Science, vol. 50, no. 16, pp. 3003–3021, 2019.

    MathSciNet  MATH  Google Scholar 

  30. P. H. Du, Y. N. Pan, H. Y. Li, and H. K. Lam, “Nonsingular finite-time event-triggered fuzzy control for large-scale nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 29, no. 8, pp. 2088–2099, 2021.

    Google Scholar 

  31. S. J. Kang, X. P. Liu, and H. Q. Wang, “Command filterbased adaptive fuzzy decentralized control for large-scale nonlinear systems,” Nonlinear Dynamics, vol. 105, no. 4, pp. 3239–3253, 2021.

    Google Scholar 

  32. A. Polyakov, “Nonlinear feedback design for fixed-time stabilization of linear control systems,” IEEE Transactions on Automatic Control, vol. 57, pp. 2106–2110, 2012.

    MathSciNet  MATH  Google Scholar 

  33. H. F. Hong, H. Wang, and Z. L. Wang, “Finite-time and fixed-time consensus problems for second-order multiagent systems with reduced state information,” Science China Information Sciences, vol. 62, Article number 212201, 2019.

    MathSciNet  Google Scholar 

  34. M. Chen, H. Q. Wang, and X. P. Liu, “Adaptive fuzzy practical fixed-time tracking control of nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 29, no. 3, pp. 664–673, 2021.

    Google Scholar 

  35. D. S. Ba, Y. X. Li, and S. C. Tong, “Fixed-time adaptive neural tracking control for a class of uncertain nonstrict nonlinear systems,” Neurocomputing, vol. 363, pp. 273–280, 2019.

    Google Scholar 

  36. Q. Zhou, P. H. Du, H. Y. Li, and R. Q. Lu, “Adaptive fixedtime control of error-constrained pure-feedback interconnected nonlinear systems,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 51, no. 10, pp. 6369–6380, 2021.

    Google Scholar 

  37. L. J. Zhang, Y. Q. **a, and G. H. Shen, “Fixed-time attitude tracking control for spacecraft based on a fixed-time extended state observer,” Science China Information Sciences, 64, Article number 212201, 2021.

    MathSciNet  Google Scholar 

  38. Q. Chen, S. **e, M. Sun, and X. He, “Adaptive nonsingular fixed-time attitude stabilization of uncertain spacecraft,” IEEE Transactions on Aerospace and Electronic Systems, vol. 54, no. 6, pp. 2937–2950, 2018.

    Google Scholar 

  39. M. Tao, Q. Chen, X. He, and M. Sun, “Adaptive fixed-time fault-tolerant control for rigid spacecraft using a double power reaching law,” International Journal of Robust and Nonlinear Control, vol. 29, no. 12, pp. 4022–4040, 2019.

    MathSciNet  MATH  Google Scholar 

  40. B. Ning, J. **, Z. Zuo, and J. Zheng, “Distributed fixed-time cooperative tracking control for multi-robot systems,” Proc. of IEEE International Conference on Robotics and Automation, pp. 833–838, 2017. DOI: https://doi.org/10.1109/ICRA.2017.7989101

    Google Scholar 

  41. C. Wang, H. Tnunay, Z. Zuo, B. Lennox, and Z. T. Ding, “Fixed-time formation control of multirobot systems: Design and experiments,” IEEE Transactions on Industrial Electronics, vol. 66, no. 8, pp. 6292–6301, 2018.

    Google Scholar 

  42. Z. Zhu, Y. Q. **a, and M. Y. Fu, “Attitude stabilization of rigid spacecraft with finite-time convergence,” International Journal of Robust and Nonlinear Control, vol. 21, no. 6, pp. 686–702, 2011.

    MathSciNet  MATH  Google Scholar 

  43. S. Y. Khoo, J. L. Yin, Z. H. Man, and X. H. Yu, “Finitetime stabilization of stochastic nonlinear systems in strictfeedback form,” Automatica, vol. 49, no. 5, pp. 1403–1410, 2013.

    MathSciNet  MATH  Google Scholar 

  44. Y. Z. Wang and G. Feng, “On finite-time stability and stabilization of nonlinear port-controlled hamiltonian systems,” Science China Information Sciences, vol. 51, pp. 1–14, 2013.

    MathSciNet  Google Scholar 

  45. X. S. Yang, J. D. Cao, C. Xu, and J. W. Feng, “Finite-time stabilization of switched dynamical networks with quantized couplings via quantized controller,” Science China Technological Sciences, vol. 61, pp. 299–308, 2018.

    Google Scholar 

  46. Z. X. Zhang and J. X. Dong, “A novel H control for T-S fuzzy systems with membership functions online optimization learning,” IEEE Transactions on Fuzzy Systems, vol. 30, no. 4, pp. 1129–1138, 2022.

    Google Scholar 

  47. Z. X. Zhang and J. X. Dong, “Fault-tolerant containment control for IT2 fuzzy networked multiagent systems against denial-of-service attacks and actuator faults,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 52, no. 4, pp. 2213–2224, 2022.

    Google Scholar 

  48. J. X. Dong, Q. H. Hou, and M. M. Ren, “Control synthesis for discrete-time T-S fuzzy systems based on membership function-dependent H performance,” IEEE Transactions on Fuzzy Systems, vol. 28, no. 12, pp. 3360–3366, 2019.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhiyao Ma.

Additional information

Bo Kang received her B.S. degree in economic statistics, and M.E. degree in applied mathematics from Liaoning University of Technology, **zhou, China, in 2019 and 2022, respectively. Her current research interests include finite-time intelligent adaptive control of high-order nonlinear systems.

Zhiyao Ma received his B.S. degree in information and computing science, M.E. degree in applied mathematics from Liaoning University of Technology, **zhou, China, and a Ph.D. degree in navigation, guidance, and control from Northeastern University, Shenyang, China, in 2013, 2017, and 2021, respectively. He is currently a Lecturer at the College of Science, Liaoning University of Technology, **zhou, China. His current research interests include adaptive control, fuzzy/neural network control, and fault-tolerant control for nonlinear systems/nonlinear fractional-order systems.

Wei Zhang received his B.S. degree in nuclear physics and nuclear technology from Jilin University, China, in 1998. At present, he is working as Deputy Chief Engineer in Dandong Dongfang Measurement and Control Technology Co., Ltd. His current research interests include online inspection analysis and automation control.

Yongming Li received his B.S. and M.S. degrees in applied mathematics from Liaoning University of Technology, **zhou, China, in 2004 and 2007, respectively. He received a Ph.D. degree in transportation information engineering & control from Dalian Maritime University, Dalian, China in 2014. He is currently a Professor in the College of Science, Liaoning University of Technology. His current research interests include adaptive control, fuzzy control, and neural networks control for nonlinear systems.

Publisher’s Note

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

This work was supported by the National Natural Science Foundation (NNSF) of China under Grant U22A2043.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kang, B., Ma, Z., Zhang, W. et al. Fixed-time Fuzzy Adaptive Decentralized Control for High-order Nonlinear Large-scale Systems. Int. J. Control Autom. Syst. 20, 4100–4110 (2022). https://doi.org/10.1007/s12555-021-1050-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-021-1050-8

Keywords

Navigation