Adaptive Finite‐Time Sliding Mode Backstepping Controller for Double‐Integrator Systems with Mismatched Uncertainties and External Disturbances

Abstract

In this paper, a novel adaptive finite‐time sliding mode backstepping (AFSMBS) control scheme is suggested to control a type of high‐order double‐integrator systems with mismatched disturbances and uncertainties. A robust sliding mode backstepping control method, adaptive control method, and finite‐time stability notion are incorporated to provide a better tracking performance over applying them individually and to use their benefits simultaneously. The concept of a sliding mode is used to define a new form of a backstepping controller. The adaptive control method is utilized to adaptively estimate the upper bounds of the disturbances and uncertainties and the estimated data are used in the control low. The notion of the finite‐time stability is incorporated with the suggested control scheme to ensure the system’s convergence within a finite time. The stability proof is obtained for the closed‐loop system in a finite time utilizing the Lyapunov stability theorem. Simulation results are obtained for an example of a remotely operated vehicle (ROV) with three degrees of freedom (3‐DOF) to demonstrate the efficacy of the suggested control approach.