Document Type: Original Research Paper


Shiraz University of Technology


In this paper, a novel approach for finite-time stabilization of uncertain affine systems is proposed. In the proposed approach, a fast terminal sliding mode (FTSM) controller is designed, based on the input-output feedback linearization of the nonlinear system with considering its internal dynamics. One of the main advantages of the proposed approach is that only the outputs and external states of the system should be measured. Moreover, in order to realize finite-time convergence of the output variables, a set of switching manifolds with a recursive procedure is utilized. Finally, robust stability and efficacy of the proposed control law are shown through computer simulations.

Graphical Abstract


[1]     I.  Utkin Vadim, “Variable structure systems with sliding modes,” IEEE Trans. Autom. Control, vol. 22, no. 2, pp. 212-222, 1977.

[2]     W. Gao and J. C. Hung, “Variable structure control of nonlinear systems: A new approach,” IEEE Trans. on Ind. Electron., vol. 40, no. 1, pp. 45–55, 1993.

[3]     C. Edwards and S. Spurgeon, Sliding mode control: Theory and applications. CRC Press, 1998.

[4]     A. Sabanovic, L. M. Fridman, and S. K. Spurgeon,"Variable structure systems: From principles to implementation," IET Digital Library, vol. 66, ISBN: 978-0-86341-350-6, 2004.

[5]     V. T. Haimo, “Finite time differential equations,” in Proc. 24th IEEE Conference on Decision and Control, vol. 24, pp. 1729–1733, Fort Lauderdale, FL., USA, 1985.

[6]     S. T. Venkataraman and S. Gulati, “Control of nonlinear systems using terminal sliding modes,” J. Dyn. Syst. Meas. Control, vol. 115, no. 3, pp. 554–560, 1993.

[7]   J. Wang , S. Li , J. Yang, B. Wu, and Q. Li ,“Finite-time disturbance observer based non singular terminal sliding-modecontrol for pulse width modulation based DC–DC buck converters with mismatched load,” IET Power Electronics, vol. 9, no. 9, pp. 1995 – 2002, 2016.

[8] Z. Mao, M. Zheng, and Y. Zhang, “Nonsingular fast terminal sliding mode control of permanent magnet linear motors,” presented at the Control and Decision Conference, Yinchuan, China, 28-30 May 2016.

 [9] T. ElmokademaM. Zribia, and K. Y. Toumi, “Terminal sliding mode control for the trajectory tracking of underactuated autonomous underwater vehicles,” Journal of Ocean Engineering, vol. 129, no. 1, pp. 613–625, 2017.

[10] H. YangaB. X. Baib, and H. Baoyina, “Finite-time control for asteroid hovering and landing via terminal sliding-mode guidance,” Journal of Acta Astronautica, vol. 132, pp. 78–89, 2017.

[11] Y. Feng, M. Zhou, X. Zheng, F. Han, and X. Yu, “Terminal sliding-mode control of induction motor speed servo systems,”  in Proc. 14th IEEE Conference on International Workshop on Variable Structure Systems (VSS), pp. 351-355, Nanjing, China,  1-4 June 2016.

 [12] T. Binazadeh and M. H. Shafiei, “Nonsingular terminal sliding-mode control of a tractor–trailer system,” Syst. Sci. Control Eng., vol. 2, no. 1, pp. 168–174, Dec. 2014.

[13] K. Zhuang, K. Zhang, H. Su, and J. Chu, "Terminal sliding mode control for high-order nonlinear dynamic systems," Journal of Zhejiang University, vol. 36, no. 5, pp. 482- 485, 2002.

[14] Y. Wu, X. Yu, and Z. Man, "Terminal sliding mode control design for uncertain dynamic systems," Systems and Control Letters vol. 34, no. 5, pp. 281–288, 1998.

[15] Y. TANG, “Terminal sliding mode control for rigid robots,” Automatica, vol. 34, no. 1, pp. 51–56, 1998.

[16] X. H. Yu and Z. H. Man, "Fast terminal sliding-mode control design for nonlinear dynamical systems,   fundamental theory and applications," IEEE Trans. on Circuits and Systems, vol. 49, no. 2, pp. 261-264, 2002.

[17] H. K. Khalil and J. W. Grizzle, Nonlinear systems, vol. 3. Prentice hall Upper Saddle River, 2002.

[18] S. P. Bhat and D. S. Bernstein, “Finite-time stability of continuous autonomous systems,” SIAM J. Control Optim., vol. 38, no. 3, pp. 751–766, 2000.

 [19] W. Lan, B. M. Chen, and Y. He, “On improvement of transient performance in tracking control for a class of nonlinear systems with input saturation,” Syst. Control Lett., vol. 55, no. 2, pp. 132–138, Feb. 2006.