# Chattering-Free Implementation of Continuous Terminal Algorithm with Implicit Euler Method

## TL;DR

This paper introduces a chattering-free implementation of the continuous terminal algorithm using an implicit Euler method, significantly reducing chattering in control inputs and outputs compared to traditional explicit methods.

## Contribution

The paper presents a novel implicit Euler-based implementation of CTA that effectively suppresses chattering, improving control smoothness and efficiency.

## Key findings

- Chattering is eliminated in control signals.
- The implicit Euler method outperforms explicit Euler in efficiency.
- Simulation results confirm the effectiveness of the proposed approach.

## Abstract

This paper proposes an efficient implementation for a continuous terminal algorithm (CTA). Although CTA is a continuous version of the famous twisting algorithm (TA), the conventional implementations of this CTA still suffer from chattering, especially when the gains and the time-step sizes are selected very large. The proposed implementation is based on an implicit Euler method and it totally suppresses the chattering. The proposed implementation is compared with the conventional explicit Euler implementation through simulations. It shows that the proposed implementation is very efficient and the chattering is suppressed both in the control input and output.