Skip to main content
SpringerLink
Log in

Prescribed Performance Finite-Time Tracking Control for Uncertain Nonlinear Systems

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

This work investigates the finite-time tracking control problem for a class of uncertain strict-feedback nonlinear systems from a new perspective. First, a novel concept called finite-time performance function (FTPF) is defined. Further, a new sufficient condition of finite-time stability is derived and the tracking error can converge to a predefined region within a finite-time interval. The design process of the proposed technique is simpler. Finally, four simulation examples are carried out to illustrate the effectiveness of presented 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. Ioannis K, Petar V K, and Morse A S, Systematic design of adaptive controllers for feedback linearizable systems, IEEE Trans. on Automatic Control, 1991, 36(11): 1241–1253.

    Article  MathSciNet  MATH  Google Scholar 

  2. Marino R, Respondek W, and Vanderschaft A J, Almost disturbance decoupling for single-input single-output nonlinear systems, IEEE Trans. on Automatic Control, 1989, 34(9): 1013–1017.

    Article  MathSciNet  MATH  Google Scholar 

  3. Qian C J and Lin W, Output feedback control of a class of nonlinear systems: A nonseparation principle paradigm, IEEE Trans. on Automatic Control, 2002, 47(10): 1710–1715.

    Article  MathSciNet  MATH  Google Scholar 

  4. Jiang D C and Jiang Z P, H1 almost disturbance decoupling with stability for uncertain nonlinear systems, Proceeding of European Control Conference, 1997, 652–657.

    Google Scholar 

  5. Xiong W J, Ho D C, Cao J D, et al., Backstepping approach to a class of hierarchical multi-agent systems with communication disturbance, IET Control Theory and Applications, 2016, 10(9): 981–988.

    Article  MathSciNet  Google Scholar 

  6. Wei Y H, Tse P W, and Yao Z, Adaptive backstepping output feedback control for a class of nonlinear fractional order systems, Nonlinear Dynamics, 2016, 86: 1047–1056.

    Article  MathSciNet  MATH  Google Scholar 

  7. Yu X M and Lin Y, Adaptive backstepping quantized control for a class of nonlinear systems, IEEE Trans. on Automatic Control, 2017, 62(2): 981–985.

    Article  MathSciNet  MATH  Google Scholar 

  8. Liu Z L, Chen B, and Lin C, Adaptive neural backstepping for a class of switched nonlinear systems without strict-feedback form, IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2017, 47(4): 1315–1320.

    Article  Google Scholar 

  9. Bechlioulis C P and Rovithakis G A, Prescribed performance adaptive control of SISO feedback linearizable systems with disturbances, Proceeding of Mediterranean Conference on Control and Automation, 2008, 1035–1040.

    Google Scholar 

  10. Bechlioulis C P and Rovithakis G A, Adaptive control with guaranteed transient and steady state tracking error bounds for strict feedback systems, Automatica, 2009, 45: 532–538.

    Article  MathSciNet  MATH  Google Scholar 

  11. Bechlioulis C P and Rovithakis G A, Prescribed performance adaptive control for multi-input multi-output affine in the control nonlinear systems, IEEE Trans. on Automatic Control, 2010, 55(5): 1220–1226.

    Article  MathSciNet  MATH  Google Scholar 

  12. Xu Y Y, Tong S C, and Li Y M, Prescribed performance fuzzy adaptive fault-tolerant control of non-linear systems with actuator faults, IET Control Theory and Applications, 2014, 8(6): 420–431.

    Article  MathSciNet  Google Scholar 

  13. Artemis K K, Zoe D, and Rovithakis G A, Prescribed performance tracking for flexible joint robots with unknown dynamics and variable elasticity, Automatica, 2013, 49: 1137–1147.

    Article  MathSciNet  MATH  Google Scholar 

  14. Song H T, Zhang T, Zhang G L, et al., Integrated interceptor guidance and control with prescribed performance, International Journal of Robust and Nonlinear Control, 2015, 25(16): 3179–3194.

    Article  MathSciNet  MATH  Google Scholar 

  15. Achilles T and Rovithakis G A, Low-complexity prescribed performance control of uncertain MIMO feedback linearizable systems, IEEE Trans. on Automatic Control, 2016, 61(7): 1946–1952.

    Article  MathSciNet  MATH  Google Scholar 

  16. Si W J, Dong X D, and Yang F F, Adaptive neural prescribed performance control for a class of strict-feedback stochastic nonlinear systems with hysteresis input, Neurocomputing, 2017, 251: 35–44.

    Article  Google Scholar 

  17. Zhai D, Xi C J, An L W, et al., Prescribed performance switched adaptive dynamic surface control of switched nonlinear systems with average dwell time, IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2017, 47(7): 1257–1269.

    Article  Google Scholar 

  18. Gai W D, Wang H L, Zhang J, et al., Adaptive neural network dynamic inversion with prescribed performance for aircraft flight control, Journal of Applied Mathematics, 2013, 2013: 1–12.

    Article  MATH  Google Scholar 

  19. Yan Z G, Zhang G S, Wang J K, et al., State and output feedback finite-time guaranteed cost control of linear Itô stochastic systems, Journal of Systems Science & Complexity, 2015, 28(4): 813–829.

    Article  MathSciNet  MATH  Google Scholar 

  20. Zhao Y, Liu Y F, Wen G H, et al., Distributed finite-time tracking of second-order multi-agent systems: An edge-based approach, IET Control Theory and Applications, 2018, 12: 149–154.

    Article  MathSciNet  Google Scholar 

  21. Liu Y F, Zhao Y, Ren W, et al., Appointed-time consensus: Accurate and practical designs, Automatica, 2018, 89: 425–429.

    Article  MathSciNet  MATH  Google Scholar 

  22. Yan Z G and Zhang W H, Finite-time stability and stabilization of Itô-type stochastic singular systems, Abstract and Applied Analysis, 2014, 2014: 1–9.

    Google Scholar 

  23. Bhat S P and Bernstein D S, Finite-time stability of continuous autonomous systems, SIAM Journal of Control and Optimation, 2000, 38(3): 751–766.

    Article  MathSciNet  MATH  Google Scholar 

  24. Huang X Q, Lin W, and Yang B, Global finite-time stabilization of a class of uncertain nonlinear systems, Automatica, 2005, 41: 881–888.

    Article  MathSciNet  MATH  Google Scholar 

  25. Zhang Z K, Duan G R, and Hou M Z, Global finite time stabilization of pure-feedback systems with input dead-zone nonlinearity, Journal of the Franklin Institute, 2017, 354: 4073–4101.

    Article  MathSciNet  MATH  Google Scholar 

  26. Wu J, Chen W S, and Li J, Global finite-time adaptive stabilization for nonlinear systems with multiple unknown control directions, Automatica, 2016, 69: 298–307.

    Article  MathSciNet  MATH  Google Scholar 

  27. Fu J, Ma R C, and Chai T Y, Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers, Automatica, 2015, 54: 360–373.

    Article  MathSciNet  MATH  Google Scholar 

  28. Hong Y G, Jiang Z P, and Feng G, Finite-time input-to-state stability and applications to finitetime control design, SIAM Journal of Control and Optimation, 2010, 48(7): 4395–4418.

    Article  MATH  Google Scholar 

  29. Zhang X F, Feng G, and Sun Y H, Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems, Automatica, 2012, 48: 499–504.

    Article  MathSciNet  MATH  Google Scholar 

  30. Wang X Y, Li S H, and Shi P, Distributed finite-time containment control for doubleintegrator multiagent systems, IEEE Trans. on Cybernetics, 2014, 44(9): 1518–1528.

    Article  Google Scholar 

  31. Huang S P and Xiang Z R, Finite-time output tracking for a class of switched nonlinear systems, International Journal of Robust and Nonlinear Control, 2016, 27(6): 1017–1038.

    Article  MathSciNet  MATH  Google Scholar 

  32. Yin J L, Khoo S Y, and Man Z H, Finite-time stability theorems of homogeneous stochastic nonlinear systems, Systems & Control Letters, 2017, 100: 6–13.

    Article  MathSciNet  MATH  Google Scholar 

  33. Wang Y J and Song S D, Leader-following control of high-order multi-agent systems under directed graphs: Pre-specified finite-time approach, Automatica, 2018, 87: 113–120.

    Article  MathSciNet  MATH  Google Scholar 

  34. Song Y D, Wang Y J, Holloway J, et al., Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite-time, Automatica, 2017, 83: 243–251.

    Article  MathSciNet  MATH  Google Scholar 

  35. Wang H H, Chen B, Lin C, et al., Adaptive finite-time control for a class of uncertain high-order non-linear systems based on fuzzy approximation, IET Control Theory and Applications, 2017, 11(5): 677–684.

    Article  MathSciNet  Google Scholar 

  36. Li J, Wu J, Guo X, et al., Global finite-time stabilization for a class of high-order nonlinear systems with multiple unknown control directions, International Journal of Control Automation and Systems, 2017, 15(1): 178–185.

    Article  Google Scholar 

  37. Nguang S K, Robust stabilization of a class of time-delay nonlinear systems, IEEE Trans. on Automatic Control, 2000, 45(4): 756–762.

    Article  MathSciNet  MATH  Google Scholar 

  38. Jia X L, Chen X K, Xu S Y, et al., Adaptive output feedback control of nonlinear time-delay systems with application to chemical reactor systems, IEEE Trans. on Industry Electronic, 2017, 64(6): 4792–4799.

    Article  Google Scholar 

  39. Zhang J X and Yang G H, Fuzzy adaptive output feedback control of uncertain nonlinear systems with prescribed performance, IEEE Trans. on Cybernetics, 2018, 48(5): 1342–1354.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

    Yuanwei Jing & Yang Liu

  2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Shaowei Zhou

Authors
  1. Yuanwei Jing
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shaowei Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yang Liu.

Additional information

This research was supported by the China Scholarship Council under Grant No. 201606080044, the National Natural Science Funds of China under Grant No. 61773108.

This paper was recommended for publication by Editor HUANG Jie.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jing, Y., Liu, Y. & Zhou, S. Prescribed Performance Finite-Time Tracking Control for Uncertain Nonlinear Systems. J Syst Sci Complex 32, 803–817 (2019). https://doi.org/10.1007/s11424-018-7287-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-018-7287-5

Keywords

Search

Navigation