Skip to main content
SpringerLink
Log in

Finite-time adaptive optimal tracking control for a QUAV

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Considering the problem of trajectory tracking control for a quadrotor unmanned aerial vehicle, the command filter-based finite-time adaptive optimal control strategy is proposed. By utilizing a finite-time command filter to rapidly approximate the derivative of virtual control signal and designing fractional power error compensating signal, the problem of “explosion of complexity” and the effect of filtered error are removed simultaneously. Furthermore, the adaptive dynamic programming technique is used to construct a critic-actor network, which enables the optimization of the compensated tracking errors and control signals. The proposed finite-time optimal control scheme ensures the minimization of the performance index function and guarantees the finite-time boundedness of all signals in closed-loop system, and the position and attitude tracking errors are driven into a sufficiently small neighborhood of the origin in a finite time. Finally, the validity and superiority of the presented finite-time adaptive optimal control algorithm are verified by a simulation example.

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
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Data availability

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

References

  1. Lian, S., Meng, W., Lin, Z., Shao, K., Zheng, J., Li, H., Lu, R.: Adaptive attitude control of a quadrotor using fast nonsingular terminal sliding mode. IEEE Trans. Ind. Electron. 69(2), 1597–1607 (2022)

    Article  Google Scholar 

  2. Wang, Y., Wang, Y., Ren, B.: Energy saving quadrotor control for field inspections. IEEE Trans. Syst. Man Cybern. Syst. 52(3), 1768–1777 (2022)

    Article  Google Scholar 

  3. Qian, L., Liu, H.H.: Path-following control of a quadrotor UAV with a cable-suspended payload under wind disturbances. IEEE Trans. Ind. Electron. 67(3), 2021–2029 (2020)

    Article  Google Scholar 

  4. Xian, B., Wang, S., Yang, S.: Nonlinear adaptive control for an unmanned aerial payload transportation system: theory and experimental validation. Nonlinear Dyn. 98(3), 1745–1760 (2019)

    Article  MATH  Google Scholar 

  5. Hua, C., Chen, J., Guan, X.: Fractional-order sliding mode control of uncertain QUAVs with time-varying state constraints. Nonlinear Dyn. 95(2), 1347–1360 (2019)

    Article  Google Scholar 

  6. Koksal, N., An, H., Fidan, B.: Backstepping-based adaptive control of a quadrotor UAV with guaranteed tracking performance. ISA Trans. 105, 98–110 (2020)

    Article  Google Scholar 

  7. Yu, G., Cabecinhas, D., Cunha, R., Silvestre, C.: Nonlinear backstepping control of a quadrotor-slung load system. IEEE/ASME Trans. Mechatron. 24(5), 2304–2315 (2019)

    Article  Google Scholar 

  8. Yu, Z., Zhang, Y., Jiang, B., Su, C.Y., Fu, J., Jin, Y., Chai, T.: Decentralized fractional-order backstepping fault-tolerant control of multi-UAVs against actuator faults and wind effects. Aerosp. Sci. Technol. 104, 105939 (2020)

    Article  Google Scholar 

  9. Xu, L.X., Ma, H.J., Guo, D., Xie, A.H., Song, D.L.: Backstepping sliding-mode and cascade active disturbance rejection control for a quadrotor UAV. IEEE/ASME Trans. Mechatron. 25(6), 2743–2753 (2020)

    Article  Google Scholar 

  10. Shao, X., Liu, J., Cao, H., Shen, C., Wang, H.: Robust dynamic surface trajectory tracking control for a quadrotor UAV via extended state observer. Int. J. Robust Nonlinear Control 28(7), 2700–2719 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  11. Fu, C., Hong, W., Lu, H., Zhang, L., Guo, X., Tian, Y.: Adaptive robust backstepping attitude control for a multi-rotor unmanned aerial vehicle with time-varying output constraints. Aerosp. Sci. Technol. 78, 593–603 (2018)

    Article  Google Scholar 

  12. Zhang, X., Wang, Y., Zhu, G., Chen, X., Li, Z., Wang, C., Su, C.Y.: Compound adaptive fuzzy quantized control for quadrotor and its experimental verification. IEEE Trans. Cybern. 51(3), 1121–1133 (2021)

    Article  Google Scholar 

  13. Shen, Z., Li, F., Cao, X., Guo, C.: Prescribed performance dynamic surface control for trajectory tracking of quadrotor UAV with uncertainties and input constraints. Int. J. Control 94(11), 2945–2955 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhao, S., Dong, W., Farrell, J.A.: Quaternion-based trajectory tracking control of VTOL-UAVs using command filtered backstepping. In: 2013 American Control Conference, pp. 1018–1023. IEEE (2013)

  15. Aboudonia, A., El-Badawy, A., Rashad, R.: Active anti-disturbance control of a quadrotor unmanned aerial vehicle using the command-filtering backstepping approach. Nonlinear Dyn. 90(1), 581–597 (2017)

    Article  MATH  Google Scholar 

  16. Li, C., Wang, Y., Yang, X.: Adaptive fuzzy control of a quadrotor using disturbance observer. Aerosp. Sci. Technol. 128, 107784 (2022)

    Article  Google Scholar 

  17. Cao, L., Wang, Y., Zhang, S., Fei, T.: Command-filtered sensor-based backstepping controller for small unmanned aerial vehicles with actuator dynamics. Int. J. Syst. Sci. 49(16), 3365–3376 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  18. Liu, K., Wang, R.: Antisaturation command filtered backstepping control-based disturbance rejection for a Quadarotor UAV. IEEE Trans. Circuits Syst. II Express Briefs 68(12), 3577–3581 (2021)

    Google Scholar 

  19. Hu, C., Zhang, Z., Zhou, X., Wang, N.: Command filter-based fuzzy adaptive nonlinear sensor-fault tolerant control for a quadrotor unmanned aerial vehicle. Trans. Inst. Meas. Control 42(2), 198–213 (2020)

    Article  Google Scholar 

  20. Murray, J.J., Cox, C.J., Lendaris, G.G., Saeks, R.: Adaptive dynamic programming. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews) 32(2), 140–153 (2002)

  21. Vamvoudakis, K.G., Lewis, F.L.: Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem. Automatica 46(5), 878–888 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  22. Zargarzadeh, H., Dierks, T., Jagannathan, S.: Optimal control of nonlinear continuous-time systems in strict-feedback form. IEEE Trans. Neural Netw. Learn. Syst. 26(10), 2535–2549 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  23. Zhao, B., Jia, L., Xia, H., Li, Y.: Adaptive dynamic programming-based stabilization of nonlinear systems with unknown actuator saturation. Nonlinear Dyn. 93(4), 2089–2103 (2018)

    Article  MATH  Google Scholar 

  24. Liu, H., Li, B., Xiao, B., Ran, D., Zhang, C.: Reinforcement learning-based tracking control for a quadrotor unmanned aerial vehicle under external disturbances. Int. J. Robust Nonlinear Control (2022). https://doi.org/10.1002/rnc.6334

    Article  Google Scholar 

  25. Gao, Q., Wei, X.T., Li, D.H., Ji, Y.H., Jia, C.: Tracking control for a quadrotor via dynamic surface control and adaptive dynamic programming. Int. J. Control Autom. Syst. 20(1), 349–363 (2022)

    Article  Google Scholar 

  26. Wen, G., Chen, C.P., Ge, S.S.: Simplified optimized backstepping control for a class of nonlinear strict-feedback systems with unknown dynamic functions. IEEE Trans. Cybern. 51(9), 4567–4580 (2021)

    Article  Google Scholar 

  27. Wen, G., Hao, W., Feng, W., Gao, K.: Optimized backstepping tracking control using reinforcement learning for quadrotor unmanned aerial vehicle system. IEEE Trans. Syst. Man Cybern. Syst. 52(8), 5004–5015 (2022)

    Article  Google Scholar 

  28. Yu, S., Yu, X., Shirinzadeh, B., Man, Z.: Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatica 41(11), 1957–1964 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  29. Liu, K., Wang, X., Wang, R., Sun, G., Wang, X.: Antisaturation finite-time attitude tracking control based observer for a quadrotor. IEEE Trans. Circuits Syst. II Express Briefs 68(6), 2047–2051 (2021)

    Google Scholar 

  30. Chen, Q., Ye, Y., Hu, Z., Na, J., Wang, S.: Finite-time approximation-free attitude control of quadrotors: theory and experiments. IEEE Trans. Aerosp. Electron. Syst. 57(3), 1780–1792 (2021)

    Article  Google Scholar 

  31. Wang, F., Gao, H., Wang, K., Zhou, C., Zong, Q., Hua, C.: Disturbance observer-based finite-time control design for a quadrotor UAV with external disturbance. IEEE Trans. Aerosp. Electron. Syst. 57(2), 834–847 (2021)

    Article  Google Scholar 

  32. Eliker, K., Grouni, S., Tadjine, M., Zhang, W.: Quadcopter nonsingular finite-time adaptive robust saturated command-filtered control system under the presence of uncertainties and input saturation. Nonlinear Dyn. 104(2), 1363–1387 (2021)

    Article  Google Scholar 

  33. Xu, Q., Wang, Z., Zhen, Z.: Adaptive neural network finite time control for quadrotor UAV with unknown input saturation. Nonlinear Dyn. 98(3), 1973–1998 (2019)

    Article  MATH  Google Scholar 

  34. Mofid, O., Mobayen, S.: Adaptive finite-time backstepping global sliding mode tracker of quad-rotor UAVs under model uncertainty, wind perturbation, and input saturation. IEEE Trans. Aerosp. Electron. Syst. 58(1), 140–151 (2022)

    Article  Google Scholar 

  35. Wang, N., Deng, Q., Xie, G., Pan, X.: Hybrid finite-time trajectory tracking control of a quadrotor. ISA Trans. 90, 278–286 (2019)

    Article  Google Scholar 

  36. Tian, B., Cui, J., Lu, H., Zuo, Z., Zong, Q.: Adaptive finite-time attitude tracking of quadrotors with experiments and comparisons. IEEE Trans. Ind. Electron. 66(12), 9428–9438 (2019)

  37. Chen, Y., Liang, J., Wu, Y., Miao, Z., Zhang, H., Wang, Y.: Adaptive sliding-mode disturbance observer-based finite-time control for unmanned aerial manipulator with prescribed performance. IEEE Trans. Cybern. (2022). https://doi.org/10.1109/TCYB.2022.3168030

  38. Beard, R.W., Saridis, G.N., Wen, J.T.: Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation. Automatica 33(12), 2159–2177 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  39. Wang, F., Chen, B., Lin, C., Zhang, J., Meng, X.: Adaptive neural network finite-time output feedback control of quantized nonlinear systems. IEEE Trans. Cybern. 48(6), 1839–1848 (2018)

    Article  Google Scholar 

  40. Yu, J., Shi, P., Zhao, L.: Finite-time command filtered backstepping control for a class of nonlinear systems. Automatica 92, 173–180 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  41. Wang, L.X.: Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Prentice-Hall, Inc., Hoboken (1994)

    Google Scholar 

  42. Qian, C., Lin, W.: A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans. Autom. Control 46(7), 1061–1079 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  43. Hardy, G.H., Littlewood, J.E., Pólya, G., Pólya, G., et al.: Inequalities. Cambridge University Press, Cambridge (1952)

    MATH  Google Scholar 

  44. Cui, G., Yu, J., Wang, Q.G.: Finite-time adaptive fuzzy control for MIMO nonlinear systems with input saturation via improved command-filtered backstepping. IEEE Trans. Syst. Man Cybern. Syst. 52(2), 980–989 (2022)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the Natural Science Fund for Excellent Young Scholars of Jiangsu Province under Grant BK20211605 and the National Natural Science Foundation of China under Grants 61703059, 61873144.

Author information

Authors and Affiliations

  1. School of Electronic and Information Engineering, Suzhou University of Science and Technology, Suzhou, 215009, China

    Wei Yang, Guozeng Cui & Shenghui Guo

  2. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, China

    Qian Ma

  3. School of Automation, Southeast University, Nanjing, 210096, China

    Jiali Ma

Authors
  1. Wei Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guozeng Cui
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qian Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jiali Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shenghui Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guozeng Cui.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, W., Cui, G., Ma, Q. et al. Finite-time adaptive optimal tracking control for a QUAV. Nonlinear Dyn 111, 10063–10076 (2023). https://doi.org/10.1007/s11071-023-08349-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-023-08349-2

Keywords

Search

Navigation