Kybernetika 48 no. 2, 206-222, 2012

Finite-time output feedback stabilization and control for a quadrotor mini-aircraft

Chuanlin Zhang, Shihua Li and Shihong Ding


This paper focuses on the finite-time output feedback control problem for a quad-rotor mini-aircraft system. First, a finite-time state feedback controller is designed by utilizing the finite-time control theory. Then, considering the case that the velocity states are not measurable, a finite-time stable observer is developed to estimate the unmeasurable states. Thus a finite-time output feedback controller is obtained and the stability analysis is provided to ensure the finite-time stability of the closed loop system. The proposed control method improves the convergence and disturbance rejection properties with respect to the asymptotically control results. Simulation results show the effectiveness of the proposed method.


output feedback, quadrotor mini-aircraft, finite-time stability, finite-time observer


93E12, 62A10


  1. K. Alexis, G. Nikolakopoulos and A. Tzes: Constrained-control of a quadrotor helicopter for trajectory tracking under wind-gust disturbances. In: Proc. 15th IEEE Mediterranean Electrotechnical Conference 2010, pp. 1411-1416.   CrossRef
  2. K. Alexis, G. Nikolakopoulos and A. Tzes: Constrained optimal attitude control of a quadrotor helicopter subject to wind-gusts: Experimental studies. In: Proc. Amer. Control Conference 2010, pp. 4451-4455.   CrossRef
  3. A. Benallegue, A. Mokhtari and L. Fridman: High-order sliding-mode observer for a quadrotor UAV. Internat. J. Robust and Nonlinear Control 18 (2008), 427-440.   CrossRef
  4. S. P. Bhat and D. S. Bernstein: Finite-time stability of homogeneous systems. In: Proc. Amer. Control Conference 1997, pp. 2513-2514.   CrossRef
  5. S. P. Bhat and D. S. Bernstein: Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Automat. Control 43 (1998), 678-682.   CrossRef
  6. S. Bouabdallah, E. Murrieri and R. Siegwart: Design and control of an indoor micro quadrotor. In: Proc. IEEE International Conference on Robotics and Automation 2004, pp. 4393-4398.   CrossRef
  7. S. Bouabdallah and R. Siegwart: Backstepping and sliding-mode techniques applied to an indoor micro quadrotors. In: Proc. IEEE International Conference on Robotics and Automation 2005, pp. 2247-2252.   CrossRef
  8. P. Castillo, A. Dzul and R. Lozano: Real-time stabilization and tracking of a four-rotor mini-aircraft. IEEE Trans. Control Systems Technol. 12 (2004), 510-516.   CrossRef
  9. L. Derafa, L. Fridman, A. Benallegue and A. Ouldali: Super twisting control algorithm for the four rotors helicopter attitude tracking problem. In: Proc. 11th International Workshop on Variable Structure Systems 2010, pp. 62-67.   CrossRef
  10. S. H. Ding, C. J. Qian and S. H. Li: Global stabilization of a class of feedforward systems with lower-order nonlinearities. IEEE Trans. Automat. Control 55 (2010), 691-696.   CrossRef
  11. S. H. Ding, C. J. Qian and S. H. Li: Global stabilization of a class of upper-triangular systems with unbounded or uncontrollable linearizations. Internat. J. Robust and Nonlinear Control 21 (2010), 271-294.   CrossRef
  12. Y. Feng, X. H. Yu and Z. H. Man: Non-singular terminal sliding mode control of rigid manipulators. Automatica 38 (2002), 2159-2167.   CrossRef
  13. M. T. Frye, S. H. Ding, C. J. Qian and S. H. Li: Global Finite-time stabilization of a PVTOL aircraft by output feedback. In: Proc. 48th IEEE Conference on Decision and Control 2009, pp. 2831-2836.   CrossRef
  14. Y. G. Hong: Finite-time stablization and stabilizability of a class of controllable systems. Systems Control Lett. 46 (2002), 231-236.   CrossRef
  15. Y. G. Hong, J. Huang and Y. S. Xu: On an output feedback finite-time stabilization problem. IEEE Trans. Automat. Control 46 (2001), 305-309.   CrossRef
  16. Y. G. Hong, Y. S. Xu and J. Huang: Finite time control for robot manipulators. Systems Control Lett. 46 (2002), 243-253.   CrossRef
  17. A. Isidori: Nonlinear Control systems: An Introduction, Lecture Notes in Control and Information Sciences. Springer, Berlin 1985.   CrossRef
  18. L. C. Lai, C. C. Yang and C. J. Wu: Time-optimal control of a hovering quad-rotor helicopter. J. Intell. and Robotic Systems 45 (2006), 115-135.   CrossRef
  19. A. Levant: Sliding order and sliding accuracy in sliding mode control. Internat. J. of Control 58 (1993), 1247-1263.   CrossRef
  20. S. H. Li, S. H. Ding and Q. Li: Global set stabilization of the spacecraft attitude using finite-time control technique. Internat. J. Control 82 (2009), 822-836.   CrossRef
  21. T. Madani and A. Benallegue: Control of a quadrotor mini-helicopter via full state backstepping technique. In: Proc. 45th IEEE Conference on Decision and Control 2006.   CrossRef
  22. T. Madani and A. Benallegue: Backstepping control with exact 2-sliding mode estimation for a quadrotor unmanned aerial vehicle. In: Proc. International Conference on Intelligent Robots and Systems (2007), 141-146.   CrossRef
  23. T. Madani and A. Benallegue: Sliding mode observer and backstepping control for a quadrotor unmanned aerial vehicles. In: Proc. Amer. Control Confer. 2007, pp. 5887-5892.   CrossRef
  24. T. M$\acute{e}$nard, E. Moulay and W. Perruquetti: A global High-gain Finite-time Observer. IEEE Trans. Automat. Control 55 (2010), 1500-1506.   CrossRef
  25. V. Mistler, A. Benallegue and N. K. M. Sirdi: Exact Linearization and Noninteracting Control of a 4 Rotors Helicopter via Dynamic Feedback. In: Proc. 2001 IEEE International Workshop on Robot and Human Interactive Communication 2001.   CrossRef
  26. W. Perruquetti, T. Floquet and E. Moulay: Finite time observers and secure communication. IEEE Trans. Automat. Control 53 (2008), 356-360.   CrossRef
  27. A. Polyakov and A. Poznyak: Reaching time estimation for ``super-twisting" second order sliding mode controller via Lyapunov function designing. IEEE Tran. Automat. Control 54 (2009), 1951-1955.   CrossRef
  28. C. J. Qian and W. Lin: A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans. Automat. Control 46 (2001), 1061-1079.   CrossRef
  29. Y. J. Shen and X. H. Xia: Semi-global finite-time observers for nonlinear systems. Automatica 44 (2008), 3152-3156.   CrossRef
  30. A. R. Teel: A nonlinear small gain theorem for the analysis of control systems with saturation. IEEE Trans. Automat. Control 41 (1996), 1256-1270.   CrossRef