Discrete-Time Implementation of Continuous Terminal Algorithm With Implicit-Euler Method

This paper proposes an alternative implementation for a continuous terminal algorithm (CTA) proposed by Torres-Gonzalez et al. The original CTA is a continuous version of the twisting algorithm (TA), which mitigates the chattering by integrating the signum functions with increased relative higher order. However, the discrete-time version of CTA resulting from conventional explicit discretization method still suffer from some magnitude of chattering. The chattering is obvious when the gains of CTA and the time-step sizes are set large. We propose an implicit Euler integration method, which totally suppresses the chattering and keeps the properties of the continuous version of CTA, such as finite time convergence and high accuracy. The efficiency of this discrete-time implementation is illustrated by comparing it to the conventional explicit method.