Skip to main content
SpringerLink
Log in

Adaptive Fuzzy Tracking Control of Stochastic Mechanical System with Input Saturation

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

The issue of adaptive fuzzy tracking control for a category of nonlinear mechanical systems with random disturbances and input saturations is studied in this paper. In the design of the controller, non-differentiable saturation nonlinearity is replaced by a smooth hyperbolic tangent function, and unknown nonlinear functions are approximated using fuzzy systems. The designed adaptive fuzzy controller can ensure that all the states in the resulting closed-loop system are bounded in probability and the generalized position and velocity of the system can respectively track the desired target trajectory as much as possible. The effectiveness of the proposed control strategy is verified using simulation results.

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

Similar content being viewed by others

References

  1. Sun, W., Wu, Y.: Modeling and finite-time tracking control for mobile manipulators with affine and holonomic constraints. J. Syst. Sci. Complex. 29(3), 589–601 (2016)

    Article  MathSciNet  Google Scholar 

  2. Yang, T., Sun, N., Chen, H., et al.: Neural network-based adaptive antiswing control of an underactuated ship-mounted crane with roll motions and input dead zones. IEEE Trans. Neural Netw. Learn. Syst. (2019). https://doi.org/10.1109/TNNLS.2019.2910580

    Article  Google Scholar 

  3. Zhang, Z., Wu, Y., Huang, J.: Differential-flatness-based finite-time anti-swing control of underactuated crane systems. Nonlinear Dyn. 87(3), 1749–1761 (2017)

    Article  Google Scholar 

  4. Sun, N., Yang, T., Fang, Y., et al.: Transportation control of double-pendulum cranes with a nonlinear quasi-PID scheme: design and experiments. IEEE Trans. Syst. Man Cybern. Syst. 49(7), 1408–1418 (2019)

    Article  Google Scholar 

  5. Sun, W., Su, S., Xia, J., et al.: Adaptive fuzzy tracking control of flexible-joint robots with full-state constraints. IEEE Trans. Syst. Man Cybern. Syst. (2018). https://doi.org/10.1109/TSMC.2018.2870642

    Article  Google Scholar 

  6. Yan, Z., Lai, X., Meng, Q., et al.: A novel robust control method for motion control of uncertain single-link flexible-joint manipulator. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2900502

    Article  Google Scholar 

  7. Sun, W., Su, S., Xia, J., et al.: Adaptive tracking control of wheeled inverted pendulums with periodic disturbances. IEEE Trans. Cybern. (2018). https://doi.org/10.1109/TCYB.2018.2884707

    Article  Google Scholar 

  8. Ren, C., Du, T., Li, G., et al.: Disturbance observer-based consensus control for multiple robotic manipulators. IEEE Access 6, 51348–51354 (2018)

    Article  Google Scholar 

  9. Li, Y., Liu, L., Feng, G.: Robust adaptive output feedback control to a class of non-triangular stochastic nonlinear systems. Automatica 89, 325–332 (2018)

    Article  MathSciNet  Google Scholar 

  10. Ren, C., Chen, L., Chen, C.L.P.: Adaptive fuzzy leader-following consensus control for stochastic multiagent systems with heterogeneous nonlinear dynamics. IEEE Trans. Fuzzy Syst. 25(1), 181–190 (2017)

    Article  Google Scholar 

  11. Xie, X., Jiang, M.: Dynamic state feedback stabilization of stochastic cascade nonlinear time-delay systems with SISS inverse dynamics. IEEE Trans. Autom. Control (2019). https://doi.org/10.1109/TAC.2019.2910166

    Article  Google Scholar 

  12. Sun, W., Su, S., Dong, G., et al.: Reduced adaptive fuzzy tracking control for high-order stochastic nonstrict feedback nonlinear system with full-state constraints. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2898204

    Article  Google Scholar 

  13. Liu, S., Zhang, J., Jiang, Z.: Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems. Automatica 43(2), 238–251 (2007)

    Article  MathSciNet  Google Scholar 

  14. Xia, J., Zhang, J., Sun, W., et al.: Finite-time adaptive fuzzy control for nonlinear systems with full state constraints. IEEE Trans. Syst. Man Cybern. Syst. 49(7), 1541–1548 (2019)

    Article  Google Scholar 

  15. Wu, Z., Cui, M., Shi, P.: Backstepping control in vector form for stochastic Hamiltonian systems. SIAM J. Control Optim. 50(2), 925–942 (2012)

    Article  MathSciNet  Google Scholar 

  16. Cui, M., Wu, Z., Xie, X., et al.: Modeling and adaptive tracking for a class of stochastic Lagrangian control systems. Automatica 49(3), 770–779 (2013)

    Article  MathSciNet  Google Scholar 

  17. Liu, Z., Wu, Y.: Modelling and adaptive tracking control for flexible joint robots with random noises. Int. J. Control 87(12), 2499–2510 (2014)

    Article  MathSciNet  Google Scholar 

  18. Chen, M., Ge, S.S., Ren, B.: Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints. Automatica 7(3), 452–465 (2011)

    Article  MathSciNet  Google Scholar 

  19. Sun, N., Liang, D., Wu, Y., et al.: Adaptive control for pneumatic artificial muscle systems with parametric uncertainties and unidirectional input constraints. IEEE Trans. Ind. Inf. (2019). https://doi.org/10.1109/TII.2019.2923715

    Article  Google Scholar 

  20. Liu, Z., Xue, L., et al.: Robust output feedback tracking control for a class of high-order time-delay nonlinear systems with input dead-zone and disturbances. Nonlinear Dyn. (2019). https://doi.org/10.1007/s11071-019-05018-1

    Article  Google Scholar 

  21. Xue, L., Liu, Z., Sun, Z., et al.: New results on robust tracking control for a class of high-order nonlinear time-delay systems. Int. J. Syst. Sci. (2019). https://doi.org/10.1080/00207721.2019.1646346

    Article  MathSciNet  Google Scholar 

  22. Du, P., Liang, H., Zhao, S., 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). https://doi.org/10.1109/TSMC.2019.2918351

    Article  Google Scholar 

  23. Zhou, Q., Wang, L., Wu, C., et al.: Adaptive fuzzy control for nonstrict-feedback systems with input saturation and output constraint. IEEE Trans. Syst. Man Cybern. Syst. 47(1), 1–12 (2017)

    Article  Google Scholar 

  24. Liang, H., Zhang, Y., Huang, T., et al.: Prescribed performance cooperative control for multi-agent systems with unknown control directions and input quantization. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2019.2893645

    Article  Google Scholar 

  25. Zhang, Y., Li, H., Sun, J., et al.: Cooperative adaptive event-triggered control for multi-agent systems with actuator failures. IEEE Trans. Syst. Cybern. Syst. (2018). https://doi.org/10.1109/TSMC.2018.2883907

    Article  Google Scholar 

  26. Li, Y., Li, K., Tong, S.: Finite-time adaptive fuzzy output feedback dynamic surface control for MIMO non-strict feedback systems. IEEE Trans. Fuzzy Syst. 27(1), 96–110 (2019)

    Article  MathSciNet  Google Scholar 

  27. Meng, M., Lam, J., Feng, J., et al.: Exponential stability analysis and \(l_1\) synthesis of positive T-S fuzzy systems with time-varying delays. Nonlinear Anal. Hybrid Syst. 24, 186–197 (2017)

    Article  MathSciNet  Google Scholar 

  28. Liang, X., Xia, J., Chen, G., et al.: Dissipativity-based sampled-data control for fuzzy Markovian jump systems. Appl. Math. Comput. 361(15), 552–564 (2019)

    MathSciNet  Google Scholar 

  29. Sun, W., Yuan, W., Shao, Y., et al.: Adaptive fuzzy control of strict-feedback nonlinear time-delay systems with full-state constraints. Int. J. Fuzzy Syst. 20(8), 2556–2565 (2018)

    Article  MathSciNet  Google Scholar 

  30. Zhang, Z., Niu, Y., Song, J., et al.: Input-to-state stabilization of interval type-2 fuzzy systems subject to cyber attacks: an observer-based adaptive sliding mode approach. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2902105

    Article  Google Scholar 

  31. Zhao, X., Wang, X., Ma, L., et al.: Fuzzy-approximation-based asymptotic tracking control for a class of uncertain switched nonlinear systems. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2912138

    Article  Google Scholar 

  32. Sun, W., Xia, J., Zhuang, G., et al.: Adaptive fuzzy asymptotically tracking control of full state constrained nonlinear system based on a novel Nussbaum-type function. J. Franklin Inst. 356, 1810–1827 (2019)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  34. Ma, H., Li, H., Liang, H., et al.: Adaptive fuzzy event-triggered control for stochastic nonlinear systems with full state constraints and actuator faults. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2896843

    Article  Google Scholar 

  35. Cao, L., Zhou, Q., Dong, G., et al.: Observer-based adaptive event-triggered control for nonstrict-feedback nonlinear systems with output constraint and actuator failures. IEEE Trans. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2895858

    Article  Google Scholar 

  36. Zhang, Z., Liang, H., Wu, C., et al.: Adaptive even-triggered output feedback fuzzy control for nonlinear networked systems with packet dropouts and random actuator failure. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2891236

    Article  Google Scholar 

  37. Sun, W., Su, S., Wu, Y., et al.: Adaptive fuzzy control with high-order barrier Lyapunov functions for high-order uncertain nonlinear systems with full-state constraints. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2018.2890256

    Article  Google Scholar 

  38. Wang, L., Mendel, J.M.: Fuzzy basis functions, universal approximation, and orthogonal least squares learning. IEEE Trans. Neural Netw. 3(5), 807–814 (1992)

    Article  Google Scholar 

  39. Wen, C., Zhou, J., Liu, Z., et al.: Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance. IEEE Trans. Autom. Control 56(7), 1672–1678 (2011)

    Article  MathSciNet  Google Scholar 

  40. Zhang, L., et al., Liang, H., Sun, Y., et al.: Adaptive event-triggered fault detection scheme for semi-Markovian jump systems with output quantization. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2912846

    Article  Google Scholar 

  41. Liang, H., et al., Zhang, Z., Ahn, C.K.: Event-triggered fault detection and isolation of discrete-time systems based on geometric technique. IEEE Trans. Circuits Syst. II Express Briefs (2019). https://doi.org/10.1109/TCSII.2019.2907706

    Article  Google Scholar 

Download references

Acknowledgements

The work was supported by National Natural Science Foundation of China under Grants 61603170, 61603231 and 11601210, Youth Science and Technology Research Foundation of the ShanXi Science and Technology Department of China under Grant 201801D221167, Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (STIP) under Grant 2019L0011.

Author information

Authors and Affiliations

  1. School of Mathematics Science, Liaocheng University, Liaocheng, China

    Wen-Xing Yuan, Wei Sun & Feng-Xia Zhang

  2. Department of Automation, Shanxi University, Taiyuan, China

    Zhen-Guo Liu

Authors
  1. Wen-Xing Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhen-Guo Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Feng-Xia Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei Sun.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yuan, WX., Sun, W., Liu, ZG. et al. Adaptive Fuzzy Tracking Control of Stochastic Mechanical System with Input Saturation. Int. J. Fuzzy Syst. 21, 2600–2608 (2019). https://doi.org/10.1007/s40815-019-00728-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-019-00728-5

Keywords

Search

Navigation