Adaptive Control Design for Euler–Lagrange Systems Using Fixed-Time Fractional Integral Sliding Mode Scheme

Abstract

This paper presents an adaptive fixed-time fractional integral control for externally disturbed Euler–Lagrange systems. In the first step of the control design, the approach of fractional-order fixed-time integral nonsingular terminal sliding mode control (FoIFxTSM) is introduced. This scheme combines the benefits of fractional calculus with integral sliding mode control, resulting in fast convergence, smooth nonsingular control inputs, and fixed-time stability. By integrating an adaptive scheme, the proposed method is used to control the dynamical system in the presence of uncertainty and external perturbations. The findings of the fixed-time stability using Lyapunov analyses are provided for the closed-loop system. The simulation results are compared with the adaptive fractional-order sliding mode control scheme, and they show the better tracking and convergence performance of the proposed method.