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quadrotor mini-aircraft; finite-time stability; finite-time observer; output feedback
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.
[1] K. Alexis, G. Nikolakopoulos, 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.
[2] K. Alexis, G. Nikolakopoulos, 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.
[3] A. Benallegue, A. Mokhtari, L. Fridman: High-order sliding-mode observer for a quadrotor UAV. Internat. J. Robust and Nonlinear Control 18 (2008), 427-440. DOI 10.1002/rnc.1225 | MR 2392132
[4] S. P. Bhat, D. S. Bernstein: Finite-time stability of homogeneous systems. In: Proc. Amer. Control Conference 1997, pp. 2513-2514.
[5] S. P. Bhat, D. S. Bernstein: Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Automat. Control 43 (1998), 678-682. DOI 10.1109/9.668834 | MR 1618028 | Zbl 0925.93821
[6] S. Bouabdallah, E. Murrieri, R. Siegwart: Design and control of an indoor micro quadrotor. In: Proc. IEEE International Conference on Robotics and Automation 2004, pp. 4393-4398.
[7] S. Bouabdallah, 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.
[8] P. Castillo, A. Dzul, R. Lozano: Real-time stabilization and tracking of a four-rotor mini-aircraft. IEEE Trans. Control Systems Technol. 12 (2004), 510-516. DOI 10.1109/TCST.2004.825052
[9] L. Derafa, L. Fridman, A. Benallegue, 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.
[10] S. H. Ding, C. J. Qian, S. H. Li: Global stabilization of a class of feedforward systems with lower-order nonlinearities. IEEE Trans. Automat. Control 55 (2010), 691-696. DOI 10.1109/TAC.2009.2037455 | MR 2654834
[11] S. H. Ding, C. J. Qian, 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. DOI 10.1002/rnc.1591 | MR 2791220 | Zbl 1213.93182
[12] Y. Feng, X. H. Yu, Z. H. Man: Non-singular terminal sliding mode control of rigid manipulators. Automatica 38 (2002), 2159-2167. DOI 10.1016/S0005-1098(02)00147-4 | MR 2134882 | Zbl 1015.93006
[13] M. T. Frye, S. H. Ding, C. J. Qian, 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.
[14] Y. G. Hong: Finite-time stablization and stabilizability of a class of controllable systems. Systems Control Lett. 46 (2002), 231-236. DOI 10.1016/S0167-6911(02)00119-6 | MR 2010240
[15] Y. G. Hong, J. Huang, Y. S. Xu: On an output feedback finite-time stabilization problem. IEEE Trans. Automat. Control 46 (2001), 305-309. DOI 10.1109/9.905699 | MR 1814578 | Zbl 0992.93075
[16] Y. G. Hong, Y. S. Xu, J. Huang: Finite time control for robot manipulators. Systems Control Lett. 46 (2002), 243-253. DOI 10.1016/S0167-6911(02)00130-5 | MR 2010242 | Zbl 0994.93041
[17] A. Isidori: Nonlinear Control systems: An Introduction, Lecture Notes in Control and Information Sciences. Springer, Berlin 1985. MR 0895138
[18] L. C. Lai, C. C. Yang, C. J. Wu: Time-optimal control of a hovering quad-rotor helicopter. J. Intell. and Robotic Systems 45 (2006), 115-135. DOI 10.1007/s10846-005-9015-3
[19] A. Levant: Sliding order and sliding accuracy in sliding mode control. Internat. J. of Control 58 (1993), 1247-1263. DOI 10.1080/00207179308923053 | MR 1250057 | Zbl 0789.93063
[20] S. H. Li, S. H. Ding, Q. Li: Global set stabilization of the spacecraft attitude using finite-time control technique. Internat. J. Control 82 (2009), 822-836. DOI 10.1080/00207170802342818 | MR 2523551
[21] T. Madani, A. Benallegue: Control of a quadrotor mini-helicopter via full state backstepping technique. In: Proc. 45th IEEE Conference on Decision and Control 2006.
[22] T. Madani, 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.
[23] T. Madani, A. Benallegue: Sliding mode observer and backstepping control for a quadrotor unmanned aerial vehicles. In: Proc. Amer. Control Confer. 2007, pp. 5887-5892.
[24] T. Ménard, E. Moulay, W. Perruquetti: A global High-gain Finite-time Observer. IEEE Trans. Automat. Control 55 (2010), 1500-1506. DOI 10.1109/TAC.2010.2045698 | MR 2668964
[25] V. Mistler, A. Benallegue, 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.
[26] W. Perruquetti, T. Floquet, E. Moulay: Finite time observers and secure communication. IEEE Trans. Automat. Control 53 (2008), 356-360. DOI 10.1109/TAC.2007.914264 | MR 2391590
[27] A. Polyakov, 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. DOI 10.1109/TAC.2009.2023781 | MR 2552835
[28] C. J. Qian, W. Lin: A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans. Automat. Control 46 (2001), 1061-1079. DOI 10.1109/9.935058 | MR 1842139 | Zbl 1012.93053
[29] Y. J. Shen, X. H. Xia: Semi-global finite-time observers for nonlinear systems. Automatica 44 (2008), 3152-3156. DOI 10.1016/j.automatica.2008.05.015 | MR 2531419 | Zbl 1153.93332
[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. DOI 10.1109/9.536496 | MR 1409471 | Zbl 0863.93073
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