Skip to main content
SpringerLink
Log in

Integral Barrier Lyapunov function-based adaptive control for switched nonlinear systems

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

This paper presents an adaptive control method for a class of uncertain strict-feedback switched nonlinear systems. First, we consider the constraint characteristics in the switched nonlinear systems to ensure that all states in switched systems do not violate the constraint ranges. Second, we design the controller based on the backstepping technique, while integral Barrier Lyapunov functions (iBLFs) are adopted to solve the full state constraint problems in each step in order to realize the direct constraints on state variables. Furthermore, we introduce the Lyapunov stability theory to demonstrate that the adaptive controller achieves the desired control goals. Finally, we perform a numerical simulation, which further verifies the significance and feasibility of the presented control scheme.

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. Lewis F L. Neural network control of robot manipulators. IEEE Expert, 1996, 11: 64–75

    Article  Google Scholar 

  2. Liu Z, Li H-X. A probabilistic fuzzy logic system for modeling and control. IEEE Trans Fuzzy Syst, 2005, 13: 848–859

    Article  Google Scholar 

  3. Cao L, Li H Y, Dong G W, et al. Event-triggered control for multiagent systems with sensor faults and input saturation. IEEE Trans Syst Man Cybern Syst, 2019. doi: 10.1109/TSMC.2019.2938216

    Google Scholar 

  4. Li X M, Zhou Q, Li P, et al. Event-triggered consensus control for multi-agent systems against false data-injection attacks. IEEE Trans Cybern, 2019. doi: 10.1109/TCYB.2019.2937951

    Google Scholar 

  5. Chen J Y, Li Z H, Ding Z T. Adaptive output regulation of uncertain nonlinear systems with unknown control directions. Sci China Inf Sci, 2019, 62: 089205

    Article  MathSciNet  Google Scholar 

  6. Lyu X J, Di L, Lin Z L, et al. Characteristic model based all-coefficient adaptive control of an AMB suspended energy storage flywheel test rig. Sci China Inf Sci, 2018, 61: 112204

    Article  Google Scholar 

  7. Yang D S, Pang Y H, Zhou B W, et al. Fault diagnosis for energy internet using correlation processing-based convolutional neural networks. IEEE Trans Syst Man Cybern Syst, 2019, 49: 1739–1748

    Article  Google Scholar 

  8. Yang D S, Li T, Xie X P, et al. Event-triggered integral sliding-mode control for nonlinear constrained-input systems with disturbances via adaptive dynamic programming. IEEE Trans Syst Man Cybern Syst, 2019. doi: 10.1109/TSMC.2019.2944404

    Google Scholar 

  9. Liu L, Liu Y J, Tong S C. Neural networks-based adaptive finite-time fault-tolerant control for a class of strict-feedback switched nonlinear systems. IEEE Trans Cybern, 2019, 49: 2536–2545

    Article  Google Scholar 

  10. Long L J, Wang Z, Zhao J. Switched adaptive control of switched nonlinearly parameterized systems with unstable subsystems. Automatica, 2015, 54: 217–228

    Article  MathSciNet  MATH  Google Scholar 

  11. Xia J W, Zhang J, Sun W, et al. Finite-time adaptive fuzzy control for nonlinear systems with full state constraints. IEEE Trans Syst Man Cybern Syst, 2019, 49: 1541–1548

    Article  Google Scholar 

  12. Xia J W, Zhang J, Feng J N, et al. Command filter-based adaptive fuzzy control for nonlinear systems with unknown control directions. IEEE Trans Syst Man Cybern Syst, 2019. doi: 10.1109/TSMC.2019.2911115

    Google Scholar 

  13. Du P H, Liang H J, Zhao S Y, et al. Neural-based decentralized adaptive finite-time control for nonlinear large-scale systems with time-varying output constraints. IEEE Trans Syst Man Cybern Syst, 2019. doi: 10.1109/TSMC.2019.2918351

    Google Scholar 

  14. Xia J, Gao H, Liu M, et al. Non-fragile finite-time extended dissipative control for a class of uncertain discrete time switched linear systems. J Franklin Institute, 2018, 355: 3031–3049

    Article  MathSciNet  MATH  Google Scholar 

  15. Liang H J, Zhang Z X, Ahn C K. Event-triggered fault detection and isolation of discrete-time systems based on geometric technique. IEEE Trans Circ Syst II, 2019. doi: 10.1109/TCSII.2019.2907706

    Google Scholar 

  16. Tee K P, Ge S S, Tay E H. Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica, 2009, 45: 918–927

    Article  MathSciNet  MATH  Google Scholar 

  17. He W, Ge S S. Vibration control of a flexible beam with output constraint. IEEE Trans Ind Electron, 2015, 62: 5023–5030

    Article  Google Scholar 

  18. Li H Y, Bai L, Wang L J, et al. Adaptive neural control of uncertain nonstrict-feedback stochastic nonlinear systems with output constraint and unknown dead zone. IEEE Trans Syst Man Cybern Syst, 2017, 47: 2048–2059

    Article  Google Scholar 

  19. Yang D S, Li T, Zhang H G, et al. Event-trigger-based robust control for nonlinear constrained-input systems using reinforcement learning method. Neurocomputing, 2019, 340: 158–170

    Article  Google Scholar 

  20. Liu Y J, Tong S C, Li D J, et al. Fuzzy adaptive control with state observer for a class of nonlinear discrete-time systems with input constraint. IEEE Trans Fuzzy Syst, 2016, 24: 1147–1158

    Article  Google Scholar 

  21. He W, Chen Y, Yin Z. Adaptive neural network control of an uncertain robot with full-state constraints. IEEE Trans Cybern, 2016, 46: 620–629

    Article  Google Scholar 

  22. Li D J, Lu S M, Liu Y J, et al. Adaptive fuzzy tracking control based barrier functions of uncertain nonlinear MIMO systems with full-state constraints and applications to chemical process. IEEE Trans Fuzzy Syst, 2018, 26: 2145–2159

    Article  Google Scholar 

  23. Song Y D, Shen Z Y, He L, et al. Neuroadaptive control of strict feedback systems with full-state constraints and unknown actuation characteristics: an inexpensive solution. IEEE Trans Cybern, 2018, 48: 3126–3134

    Article  Google Scholar 

  24. Liu Y J, Lu S M, Tong S C, et al. Adaptive control-based Barrier Lyapunov functions for a class of stochastic nonlinear systems with full state constraints. Automatica, 2018, 87: 83–93

    Article  MathSciNet  MATH  Google Scholar 

  25. Zhao K, Song Y D, Ma T, et al. Prescribed performance control of uncertain euler-lagrange systems subject to full-state constraints. IEEE Trans Neural Netw Learning Syst, 2018, 29: 3478–3489

    Article  MathSciNet  Google Scholar 

  26. Liang H J, Zhang Y H, Huang T W, et al. Prescribed performance cooperative control for multiagent systems with input quantization. IEEE Trans Cybern, 2019. doi: 10.1109/TCYB.2019.2893645

    Google Scholar 

  27. Tang Z L, Tee K P, He W. Tangent Barrier Lyapunov functions for the control of output-constrained nonlinear systems. IFAC Proc Volumes, 2013, 46: 449–455

    Article  Google Scholar 

  28. Jin X. Adaptive fault tolerant control for a class of input and state constrained MIMO nonlinear systems. Int J Robust Nonlin Control, 2016, 26: 286–302

    Article  MathSciNet  MATH  Google Scholar 

  29. Tee K P, Ge S S. Control of state-constrained nonlinear systems using integral Barrier Lyapunov functionals. In: Proceedings of IEEE 51st IEEE Conference on Decision and Control (CDC), Maui, 2012. 3239–3244

    Google Scholar 

  30. He W, Zhang S, Ge S S. Adaptive control of a flexible crane system with the boundary output constraint. IEEE Trans Ind Electron, 2014, 61: 4126–4133

    Article  Google Scholar 

  31. Liu Y J, Tong S C, Chen C L P, et al. Adaptive NN control using integral Barrier Lyapunov functionals for uncertain nonlinear block-triangular constraint systems. IEEE Trans Cybern, 2017, 47: 3747–3757

    Article  Google Scholar 

  32. Tee K P, Ren B B, Ge S S. Control of nonlinear systems with time-varying output constraints. Automatica, 2011, 47: 2511–2516

    Article  MathSciNet  MATH  Google Scholar 

  33. He W, Huang H, Ge S S. Adaptive neural network control of a robotic manipulator with time-varying output constraints. IEEE Trans Cybern, 2017, 47: 3136–3147

    Article  Google Scholar 

  34. Liu Y J, Zeng Q, Tong S C, et al. Adaptive neural network control for active suspension systems with time-varying vertical displacement and speed constraints. IEEE Trans Ind Electron, 2019, 66: 9458–9466

    Article  Google Scholar 

  35. Zhai D, An L W, Dong J X, et al. Switched adaptive fuzzy tracking control for a class of switched nonlinear systems under arbitrary switching. IEEE Trans Fuzzy Syst, 2018, 26: 585–597

    Article  Google Scholar 

  36. Li S, Ahn C K, Xiang Z. Sampled-data adaptive output feedback fuzzy stabilization for switched nonlinear systems with asynchronous switching. IEEE Trans Fuzzy Syst, 2019, 27: 200–205

    Article  Google Scholar 

  37. Liu L, Liu Y J, Tong S C. Fuzzy-based multierror constraint control for switched nonlinear systems and its applications. IEEE Trans Fuzzy Syst, 2019, 27: 1519–1531

    Article  Google Scholar 

  38. Niu B, Wang D, Alotaibi N D, et al. Adaptive neural state-feedback tracking control of stochastic nonlinear switched systems: an average dwell-time method. IEEE Trans Neural Netw Learn Syst, 2019, 30: 1076–1087

    Article  MathSciNet  Google Scholar 

  39. Liu L, Liu Y J, Li D, et al. Barrier Lyapunov function-based adaptive fuzzy FTC for switched systems and its applications to resistance-inductance-capacitance circuit system. IEEE Trans Cybern, 2019. doi: 10.1109/TCYB.2019.2931770

    Google Scholar 

  40. Han Z Y, Niu B. Adaptive neural network tracking control for a class of output-constrained nonlinear switched systems. In: Proceedings of 2016 35th Chinese Control Conference (CCC), Chengdu, 2016. 2307–2312

    Chapter  Google Scholar 

  41. Niu B, Wang D, Li H, et al. A novel neural-network-based adaptive control scheme for output-constrained stochastic switched nonlinear systems. IEEE Trans Syst Man Cybern Syst, 2019, 49: 418–432

    Article  Google Scholar 

  42. Yin S, Yu H, Shahnazi R, et al. Fuzzy adaptive tracking control of constrained nonlinear switched stochastic purefeedback systems. IEEE Trans Cybern, 2017, 47: 579–588

    Article  Google Scholar 

  43. Sun K K, Mou S S, Qiu J B, et al. Adaptive fuzzy control for nontriangular structural stochastic switched nonlinear systems with full state constraints. IEEE Trans Fuzzy Syst, 2019, 27: 1587–1601

    Article  Google Scholar 

  44. Zhao X D, Zheng X L, Niu B, et al. Adaptive tracking control for a class of uncertain switched nonlinear systems. Automatica, 2015, 52: 185–191

    Article  MathSciNet  MATH  Google Scholar 

  45. Wu J, Su B Y, Li J, et al. Global adaptive neural tracking control of nonlinear MIMO systems. Neural Comput Applic, 2017, 28: 3801–3813

    Article  Google Scholar 

  46. Li D P, Liu L, Liu Y J, et al. Fuzzy approximation-based adaptive control of nonlinear uncertain state constrained systems with time-varying delays. IEEE Trans Fuzzy Syst, 2019. doi: 10.1109/TFUZZ.2019.2919490

    Google Scholar 

  47. Li D P, Chen C L P, Liu Y J, et al. Neural network controller design for a class of nonlinear delayed systems with time-varying full-state constraints. IEEE Trans Neural Netw Learn Syst, 2019. doi: 10.1109/TNNLS.2018.2886023

    Google Scholar 

  48. Long L J, Zhao J. Adaptive output-feedback neural control of switched uncertain nonlinear systems with average dwell time. IEEE Trans Neural Netw Learn Syst, 2015, 26: 1350–1362

    Article  MathSciNet  Google Scholar 

  49. Chen A Q, Tang L, Liu Y J, et al. Adaptive control for switched uncertain nonlinear systems with time-varying output constraint and input saturation. Int J Adapt Control Signal Process, 2019, 33: 1344–1358

    Article  MathSciNet  MATH  Google Scholar 

  50. Long L J, Zhao J. Adaptive fuzzy output-feedback dynamic surface control of MIMO switched nonlinear systems with unknown gain signs. Fuzzy Sets Syst, 2016, 302: 27–51

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61803190, 61973147, 61773188, 61751202) and Fundamental Research Funds for the Universities of Liaoning Province (Grant No. JZL201715402).

Author information

Authors and Affiliations

  1. College of Science, Liaoning University of Technology, Jinzhou, 121001, China

    Lei Liu, Yan-Jun Liu, Aiqing Chen & Shaocheng Tong

  2. Computer Science and Engineering, South China University of Technology, Guangzhou, 510641, China

    C. L. Philip Chen

  3. Navigation College, Dalian Maritime University, Dalian, 116026, China

    C. L. Philip Chen

Authors
  1. Lei Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yan-Jun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aiqing Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shaocheng Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. C. L. Philip Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yan-Jun Liu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, L., Liu, YJ., Chen, A. et al. Integral Barrier Lyapunov function-based adaptive control for switched nonlinear systems. Sci. China Inf. Sci. 63, 132203 (2020). https://doi.org/10.1007/s11432-019-2714-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-019-2714-7

Keywords

Search

Navigation