Fixed‐time backstepping control design for high‐order strict‐feedback non‐linear systems via terminal sliding mode

Abstract

In this study, the state feedback fixed-time control problem is addressed for a class of high-order strict-feedback non-linear systems (SFNSs) with mismatching system uncertainties. Based on the fixed-time control technique and uniform exact difference method, a new fixed-time tracking control algorithm via the backstepping method in conjunction with a novel second-order sliding mode super-twisting-like structure adaptive fixed-time disturbance observer is proposed. Compared with many existing finite-time control results in which the convergence time grows unboundedly when the system initial conditions grow, the fixed-time control provides faster convergence rate by using high-degree terms and the settling time function derived only with controller parameters, is allowed to be adjusted independently of the system initial conditions. Moreover, to avoid the computation explosion, the singularity problem and to relax the assumption on the mismatching system uncertainties, the dynamics surface control method is employed based on a novel non-linear non-smooth first-order filter. Then the semi-globally uniformly fixed-time convergent performance of the high-order SFNSs is achieved. Finally, theoretical results are supported by simulation and experimental results.