Fixed-time backstepping control based on adaptive super-twisting disturbance observers for a class of nonlinear systems

This paper proposes a fixed-time backstepping control strategy based on adaptive super-twisting disturbance observers (ASTDOs) for a class of non-integral cascade high-order uncertain nonlinear systems. First, the ASTDOs are designed to estimate the system disturbances in fixed time, and the adaptive method relaxes the assumption about the system disturbances, which is that the upper bound of the first and second derivatives of the disturbance is unknown. Then we present a backstepping control strategy via an improved distributed fast terminal sliding mode, which not only guarantees that the sliding mode surface of each step is independent of one another, but also makes the system states converge in fixed time. Furthermore, to avoid the 'differential explosion' problem and the singularity problem, the dynamics surface control method is constituted. Theoretical analysis shows that the closed-loop system is semi-globally uniformly ultimately fixed-time bounded. Finally, simulation results show the validity of the proposed control strategy.