Nonlinear Dynamics

, Volume 98, Issue 3, pp 1973–1998 | Cite as

Adaptive neural network finite time control for quadrotor UAV with unknown input saturation

  • Qingzheng Xu
  • Zhisheng WangEmail author
  • Ziyang Zhen
Original paper


This study presents a novel adaptive robust control strategy for the position and attitude tracking of quadrotor unmanned aerial vehicles (UAVs) in the presence of input saturation, unmodeled nonlinear dynamics, and external disturbances. To deal with the negative effects of completely unknown input saturation constraints, a nonsymmetric saturation nonlinearity approxiator constructed by the hyperbolic tangent function attached with a parameter adjustment mechanism is incorporated into the controller design. Then, a novel neural network (NN) finite time backstepping-based anti-saturation control approach is proposed by introducing the NN finite time backstepping, designing the new virtual control signals and the modified error compensation mechanism. The proposed approach not only holds the advantages of the NN finite time backstepping control, but also prevents the system from degradation or even instability caused by unknown nonsymmetric saturation nonlinearities in actuator. The finite time convergence of all signals in the closed-loop aircraft system is guaranteed via Lyapunov finite time methodology despite the input saturations, unmodeled dynamics, and external disturbances. Finally, numerical simulations are carried out to illustrate the effectiveness and robustness of the proposed controller.


Quadrotor UAVs Backstepping Neural network Finite time convergence Input saturation nonlinearity 



This research was supported by the National Natural Science Foundation of China (61473144).

Compliance with ethical standards

Conflict of interest

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.


  1. 1.
    Rios, H., Falcon, R., Gonzalez, O.A., Dzul, A.: Continuous sliding-mode control strategies for quadrotor robust tracking: real-time application. IEEE Trans. Ind. Electron. 66(2), 1264–1272 (2019)Google Scholar
  2. 2.
    Zhao, Z., Wang, X., Yao, P., Xu, J., Yu, J.: Fuzzy health degree-based dynamic performance evaluation of quadrotors in the presence of actuator and sensor faults. Nonlinear Dyn. 95(3), 2477–2490 (2019)Google Scholar
  3. 3.
    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)Google Scholar
  4. 4.
    Hua, C.C., Wang, K., Chen, J.N., You, X.: Tracking differentiator and extended state observer-based nonsingular fast terminal sliding mode attitude control for a quadrotor. Nonlinear Dyn. 94(1), 343–354 (2018)Google Scholar
  5. 5.
    Li, C., Zhang, Y., Li, P.: Full control of a quadrotor using parameter-scheduled backstepping method: implementation and experimental tests. Nonlinear Dyn. 89(2), 1259–1278 (2017)Google Scholar
  6. 6.
    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)zbMATHGoogle Scholar
  7. 7.
    Zhu, W., Du, H., Cheng, Y., Chu, Z.: Hovering control for quadrotor aircraft based on finite-time control algorithm. Nonlinear Dyn. 88(4), 2359–2369 (2017)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Kocer, B.B., Tjahjowidodo, T., Seet, G.G.L.: Model predictive UAV-tool interaction control enhanced by external forces. Mechatronics 58, 47–57 (2019)Google Scholar
  9. 9.
    Zhou, B., Li, Z., Zheng, Z., Tang, S.: Nonlinear adaptive tracking control for a small-scale unmanned helicopter using a learning algorithm with the least parameters. Nonlinear Dyn. 89(2), 1289–1308 (2017)zbMATHGoogle Scholar
  10. 10.
    Ma, H.J., Liu, Y., Li, T., Yang, G.H.: Nonlinear high-gain observer-based diagnosis and compensation for actuator and sensor faults in a quadrotor unmanned aerial vehicle. IEEE Trans. Ind. Inform. 15(1), 550–562 (2019)Google Scholar
  11. 11.
    Sun, M., Liu, J., Wang, H., Nian, X., Xiong, H.: Robust fuzzy tracking control of a quad-rotor unmanned aerial vehicle based on sector linearization and interval matrix approaches. ISA Trans. 80, 336–349 (2018)Google Scholar
  12. 12.
    Hua, C., Chen, J., Guan, X.: Adaptive prescribed performance control of QUAVs with unknown time-varying payload and wind gust disturbance. J. Frankl. Inst. Eng. Appl. Math. 355(14), 6323–6338 (2018)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Hou, Z., Fantoni, I.: Interactive leader–follower consensus of multiple quadrotors based on composite nonlinear feedback control. IEEE Trans Control Syst. Technol. 26(5), 1732–1743 (2018)Google Scholar
  14. 14.
    Yu, J., Zhao, L., Yu, H., Lin, C., Dong, Wenjie: Fuzzy finite-time command filtered control of nonlinear systems with input saturation. IEEE Trans. Cybern. 48(8), 2378–2387 (2018)Google Scholar
  15. 15.
    Mokhtari, A., Benallegue, A., Daachi, B.: Robust feedback linearization and GH controller for a quadrotor unmanned aerial vehicle. In: 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2005 (IROS 2005). IEEE, pp. 1198–1203 (2005)Google Scholar
  16. 16.
    Heng, X., Cabecinhas, D., Cunha, R., Silvestre, C., Qingsong, X.: A trajectory tracking LQR controller for a quadrotor: design and experimental evaluation. In: TENCON 2015–2015 IEEE Region 10 Conference. IEEE, pp. 1–7 (2015)Google Scholar
  17. 17.
    Kendoul, F., Lara, D., Fantoni, I., Lozano, R.: Real-time nonlinear embedded control for an autonomous quadrotor helicopter. J. Guid. Control Dyn. 30(4), 1049–1061 (2007)Google Scholar
  18. 18.
    Guerrero-Castellanos, J.F., Marchand, N., Hably, A., Lesecq, S., Delamare, J.: Bounded attitude control of rigid bodies: real-time experimentation to a quadrotor mini-helicopter. Control Eng. Pract. 19(8), 790–797 (2011)Google Scholar
  19. 19.
    López-Araujo, D.J., Zavala-Río, A., Fantoni, I., Salazar, S., Lozano, R.: Global stabilisation of the PVTOL aircraft with lateral force coupling and bounded inputs. Int. J. Control 83(7), 1427–1441 (2010)MathSciNetzbMATHGoogle Scholar
  20. 20.
    Cao, N., Lynch, A.F.: Inner–outer loop control for quadrotor UAVs with input and state constraints. IEEE Trans. Control Syst. Technol. 24(5), 1797–1804 (2016)Google Scholar
  21. 21.
    Li, S., Wang, Y., Tan, J.: Adaptive and robust control of quadrotor aircrafts with input saturation. Nonlinear Dyn. 89(1), 255–265 (2017)zbMATHGoogle Scholar
  22. 22.
    Ofodile, N.A., Turner, M.C.: Anti-windup design for input-coupled double integrator systems with application to quadrotor UAV’s. Eur. J. Control 38, 22–31 (2017)MathSciNetzbMATHGoogle Scholar
  23. 23.
    Huang, Y., Zheng, Z., Sun, L., Zhu, M.: Saturated adaptive sliding mode control for autonomous vessel landing of a quadrotor. IET Control Theory Appl. 12(13), 1830–1842 (2018)MathSciNetGoogle Scholar
  24. 24.
    Wentao, X., Shaojun, T., Hui Y. .: Robust trajectory tracking control for a quadrotor based on a composite sliding mode control method. In: 2018 37th Chinese Control Conference (CCC), pp. 919–924 (2018)Google Scholar
  25. 25.
    Zhou, F., Zhou, Y.J., Jiang, G.P., Cao, N. .: Adaptive tracking control of quadrotor UAV system with input constraints. In: 2018 Chinese Control And Decision Conference (CCDC), pp. 5774–5779 (2018)Google Scholar
  26. 26.
    Wang, X., Su, X., Sun, L.: Disturbance observer-based singularity-free trajectory tracking control of uncertain quadrotors with input saturation. In: 2018 Chinese Control And Decision Conference (CCDC), pp. 5780–5785 (2018)Google Scholar
  27. 27.
    Faessler, M., Falanga, D., Scaramuzza, D.: Thrust mixing, saturation, and body-rate control for accurate aggressive quadrotor flight. IEEE Robot. Autom. Lett. 2(2), 476–482 (2017)Google Scholar
  28. 28.
    Tran, T.T., Sam, S., He, W., Luu-Trung-Duong, P., Truong, N.V.: Trajectory tracking control of a quadrotor aerial vehicle in the presence of input constraints. Int. J Control Autom. Syst. 16(6), 2966–2976 (2018)Google Scholar
  29. 29.
    Tran, T.T., Ge, S.S., He, W.: Adaptive control of a quadrotor aerial vehicle with input constraints and uncertain parameters. Int. J. Control 91(5), 1140–1160 (2018)MathSciNetzbMATHGoogle Scholar
  30. 30.
    Wang, W.: Trajectory tracking control of a 6-DOF quadrotor UAV with input saturation via backstepping. J. Frankl. Inst. Eng. Appl. Math. 355(7), 3288–3309 (2018)MathSciNetzbMATHGoogle Scholar
  31. 31.
    Shahvali, M., Pariz, N., Akbariyan, M.: Distributed finite-time control for arbitrary switched nonlinear multi-agent systems: an observer-based approach. Nonlinear Dyn. 94(3), 2127–2142 (2018)zbMATHGoogle Scholar
  32. 32.
    Liu, Y., Liu, X., Jing, Y., Zhang, Z.: A novel finite-time adaptive fuzzy tracking control scheme for nonstrict feedback systems. IEEE Trans. Fuzzy Syst. 27(4), 646–658 (2019)Google Scholar
  33. 33.
    Xin, Q., Shi, Z.: Robust adaptive backstepping controller design for aircraft autonomous short landing in the presence of uncertain aerodynamics. J. Aerosp. Eng. 31(2), 04018005 (2018)Google Scholar
  34. 34.
    Wu, D., Chen, M., Gong, H.: Robust control of post-stall pitching maneuver based on finite-time observer. ISA Trans. 70, 53–63 (2017)Google Scholar
  35. 35.
    Guo, Y., Guo, J.H., Song, S.M.: Backstepping control for attitude tracking of the spacecraft under input saturation. Acta Astronaut. 138, 318–325 (2017)Google Scholar
  36. 36.
    Cai, M., Xiang, Z.: Adaptive finite-time control of a class of non-triangular nonlinear systems with input saturation. Neural Comput. Appl. 29(7), 565–576 (2018)Google Scholar
  37. 37.
    Chen, L., Li, C., Sun, Y., Ma, G.: Distributed finite-time tracking control for multiple uncertain Euler–Lagrange systems with input saturations and error constraints. IET Control Theory Appl. 13(1), 123–133 (2019)MathSciNetGoogle Scholar
  38. 38.
    Ni, J., Liu, L., He, W., Liu, C.: Adaptive dynamic surface neural network control for nonstrict-feedback uncertain nonlinear systems with constraints. Nonlinear Dyn. 94(1), 165–184 (2018)zbMATHGoogle Scholar
  39. 39.
    Song, Y., Zhou, S.: Neuroadaptive control with given performance specifications for MIMO strict-feedback systems under nonsmooth actuation and output constraints. IEEE Trans. Neural Netw. Learn. Syst. 29(9), 4414–4425 (2018)Google Scholar
  40. 40.
    Luo, J., Wei, C., Dai, H., Yuan, J.: Robust LS-SVM-based adaptive constrained control for a class of uncertain nonlinear systems with time-varying predefined performance. Commun. Nonlinear Sci. Numer. Simul. 56, 561–587 (2018)MathSciNetGoogle Scholar
  41. 41.
    Zhang, Q., Wang, C., Xu, D.: Finite-time stabilization for a class of non-affine nonlinear systems with input saturation and time-varying output constraints. IEEE Access 6, 23529–23539 (2018)Google Scholar
  42. 42.
    Jiang, T., Lin, D., Song, T.: Finite-time backstepping control for quadrotors with disturbances and input constraints. IEEE Access 6, 62037–62049 (2018)Google Scholar
  43. 43.
    Fu, C., Tian, Y., Huang, H., Zhang, L., Peng, C.: Finite-time trajectory tracking control for a 12-rotor unmanned aerial vehicle with input saturation. ISA Trans. 81, 52–62 (2018)Google Scholar
  44. 44.
    Zou, A.M., Kumar, K.D.: Finite-time attitude control for rigid spacecraft subject to actuator saturation. Nonlinear Dyn. 96(2), 1017–1035 (2019)Google Scholar
  45. 45.
    Zheng, Z., Xie, L.: Finite-time path following control for a stratospheric airship with input saturation and error constraint. Int. J. Control 92(2), 368–393 (2019)MathSciNetzbMATHGoogle Scholar
  46. 46.
    Zou, A.M., de Ruiter, A.H.J., Kumar, K.D.: Disturbance observer-based attitude control for spacecraft with input MRS. IEEE Trans. Aerosp. Electron. Syst. 55(1), 384–396 (2019)Google Scholar
  47. 47.
    Su, H., Zhang, W.: Adaptive fuzzy control of MIMO nonstrict-feedback nonlinear systems with fuzzy dead zones and time delays. Nonlinear Dyn. 95(2), 1565–1583 (2019)MathSciNetGoogle Scholar
  48. 48.
    Niu, J., Chen, F., Tao, G.: Nonlinear fuzzy fault-tolerant control of hypersonic flight vehicle with parametric uncertainty and actuator fault. Nonlinear Dyn. 92(3), 1299–1315 (2018)zbMATHGoogle Scholar
  49. 49.
    Han, Y., Yu, J., Zhao, L., Yu, H., Lin, C.: Finite-time adaptive fuzzy control for induction motors with input saturation based on command filtering. IET Control Theory Appl. 12(15), 2148–2155 (2018)MathSciNetGoogle Scholar
  50. 50.
    Xia, K., Huo, W.: Adaptive control for spacecraft rendezvous subject to actuator faults and saturations. ISA Trans. 80, 176–186 (2018)Google Scholar
  51. 51.
    Zhao, S., Liang, H., Du, P., Qi, S.: Adaptive NN finite-time tracking control of output constrained nonlinear system with input saturation. Nonlinear Dyn. 92(4), 1845–1856 (2018)zbMATHGoogle Scholar
  52. 52.
    Xu, B.: Composite learning finite-time control with application to quadrotors. IEEE Trans. Syst. Man Cybern. Syst. 48(10), 1806–1815 (2018)Google Scholar
  53. 53.
    Wu, H.: Simple adaptive robust output tracking control schemes of uncertain parametric strict-feedback non-linear systems with unknown input saturations. IET Control Theory Appl. 12(12), 1694–1703 (2018)MathSciNetGoogle Scholar
  54. 54.
    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)zbMATHGoogle Scholar
  55. 55.
    Aghababa, M.P.: Finite time control of a class of nonlinear switched systems in spite of unknown parameters and input saturation. Nonlinear Anal. Hybrid Syst. 31, 220–232 (2019)MathSciNetzbMATHGoogle Scholar
  56. 56.
    Moradvandi, A., Shahrokhi, M., Malek, S.A.: Adaptive fuzzy decentralized control for a class of MIMO large-scale nonlinear state delay systems with unmodeled dynamics subject to unknown input saturation and infinite number of actuator failures. Inf. Sci. 475, 121–141 (2019)MathSciNetGoogle Scholar
  57. 57.
    Xiao, B., Yin, S.: A new disturbance attenuation control scheme for quadrotor unmanned aerial vehicles. IEEE Trans. Ind. Inform. 13(6), 2922–2932 (2017)Google Scholar
  58. 58.
    Bhat, S.P., Bernstein, D.S.: Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38(3), 751–766 (2000)MathSciNetzbMATHGoogle Scholar
  59. 59.
    Yu, S.H., Yu, X.H., Shirinzadeh, B., Man, Z.H.: Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatica 41(11), 1957–1964 (2005)MathSciNetzbMATHGoogle Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.College of Automation EngineeringNanjing University of Aeronautics and AstronauticsNanjingPeople’s Republic of China

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