Journal of Systems Engineering and Electronics ›› 2023, Vol. 34 ›› Issue (3): 775-782.doi: 10.23919/JSEE.2023.000071


Revised barrier function-based adaptive finite- and fixed-time convergence super-twisting control

Dakai LIU(), Sven ESCHE()   

  1. 1 Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken 07030, USA
  • Received:2021-09-06 Online:2023-06-15 Published:2023-06-30
  • Contact: Dakai LIU;
  • About author:
    LIU Dakai was born in 1990. He received his B.S. and M.S. degrees in navigation, guidance, and control from Northwestern Polytechnical University in 2013, 2016, respectively. He is currently pursuing his Ph.D. degree in Stevens Institute of Technology. His research interests are robust adaptive control and intelligent control. E-mail:

    ESCHE Sven was born in 1964. He received his B.S. degree in applied mechanics from Chemnitz University of Technology in Chemnitz, Germany, in 1989 and M.S. and Ph.D. degrees in mechanical engineering from Ohio State University in Columbus, Ohio, USA, in 1994 and 1997, respectively. He currently holds a position as associate professor of mechanical engineering at Stevens Institute of Technology in Hoboken, NJ, USA. His research interests include multiple subdisciplines of mechanical engineering as well as educational technologies and pedagogical approaches. E-mail:


This paper presents an adaptive gain, finite- and fixed-time convergence super-twisting-like algorithm based on a revised barrier function, which is robust to perturbations with unknown bounds. It is shown that this algorithm can ensure a finite- and fixed-time convergence of the sliding variable to the equilibrium, no matter what the initial conditions of the system states are, and maintain it there in a predefined vicinity of the origin without violation. Also, the proposed method avoids the problem of overestimation of the control gain that exists in the current fixed-time adaptive control. Moreover, it shows that the revised barrier function can effectively reduce the computation load by obviating the need of increasing the magnitude of sampling step compared with the conventional barrier function. This feature will be beneficial when the algorithm is implemented in practice. After that, the estimation of the fixed convergence time of the proposed method is derived and the impractical requirement of the preceding fixed-time adaptive control that the adaptive gains must be large enough to engender the sliding mode at time $ t = 0 $ is discarded. Finally, the outperformance of the proposed method over the existing counterpart method is demonstrated with a numerical simulation.

Key words: super-twisting algorithm, barrier function, fixed-time sliding mode control, adaptive control