Fractional‐order integral terminal sliding‐mode control for perturbed nonlinear systems with application to quadrotors

Abstract

In this article, a novel fractional‐order recursive integral terminal sliding mode (FORITSM) control is proposed for nonlinear systems in the presence of external disturbances with unknown bounds. The proposed control approach provides an easy‐to implement solution capable of zeroing the sliding variable in a finite‐time (FnT) by adding a fractional‐order command filter. Moreover, the reaching phase is eliminated, and FnT convergence of the system states is proved. The proposed technique has also a chattering alleviation property, which is beneficial for practical cases, as the control of quadrotor UAVs presented in the article. Finally, a simulation case study on a quadrotor system is illustrated to show the effectiveness of the proposed FORITSM control, also with respect to classical methods.

Recursive integral terminal sliding mode control with combined extended state observer and adaptive Kalman filter for MEMS gyroscopes

“…The sliding mode variable can be rewritten as λ = σ + 𝜌 σI (14) with σ = ̇ê + 𝓁 ê + 𝛾| ê| 𝛼 sign( ê) and ̇σ…”

“…Remark 6. It is observed from the sliding mode manifold (14) that λ(0) = 0 when σI (0) = − σ(0)∕𝜌, such that faster convergence will be achieved when the control system is forced to start from the sliding surface at the initial time with σI (0) = −…”

“…Theorem 1. With Lemma 1 and Assumptions 1-4, if the combined observer ( 7) and ( 9), the RTSMC manifold (14) and the controller ( 16) are designed for the dynamics ( 1), 𝝀 will converge to the region 𝚪 in the finite time T 0 .…”

Editorial

“…Labbadi et al 5 proposed a FO command filtered‐based recursive finite‐time control using a non‐singular TSM technique for high‐order uncertain nonlinear systems under disturbances with unknown bounds. The proposed control is developed to go beyond the limitations of existing finite‐time tracking controllers.…”

“…To compensate for the DO estimation errors, IT2FNN learning mechanisms are introduced to improve the FTCC capability. Simulation results show that all follower UAVs successfully converge into the convex hull spanned by the leader UAVs without collisions even when a portion of the UAVs encounter faults.Labbadi et al 5 proposed a FO command filtered-based recursive finite-time control using a non-singular TSM technique for high-order uncertain nonlinear systems under disturbances with unknown bounds. The proposed control is developed to go beyond the limitations of existing finite-time tracking controllers.…”