ABSTRACT

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.

摘要

针对一类非积分级联高阶不确定非线性系统，提出了一种基于自适应超扭曲扰动观测器（ASTDO）的固定时间反步控制策略。首先，ASTDO被设计为在固定时间内估计系统扰动，自适应方法放宽了系统扰动的假设，即扰动的一阶和二阶导数的上界是未知的。然后我们通过改进的分布式快速终端滑模提出了一种反步控制策略，该策略不仅保证了每一步的滑模面相互独立，而且使系统状态在固定时间内收敛。此外，为了避免“微分爆炸”问题和奇异性问题，构造了动力学曲面控制方法。理论分析表明，闭环系统是半全局一致最终固定时间有界的。最后，仿真结果表明了所提控制策略的有效性。