基于新型固定时间稳定方法的一类二阶非线性系统镇定控制

Stabilization control for a class of second order nonlinear system using a new fixed-time stable method

本文研究了受未知外部扰动侵袭的一类二阶非线性系统的固定时间镇定控制问题.首先,提出了一种新的固定时间稳定方法,并给出了收敛时间及其上界估计值的计算公式.理论分析表明,收敛时间的上界与系统初始状态无关,可由系统参数完全确定.然后,基于所提出的固定时间稳定方法设计了新型滑模趋近律和终端滑模面,使得系统状态能够在有界的有限时间内,从任意初始状态收敛至滑模面并沿着滑模面收敛至原点,同时引入了基于系统状态的自适应切换方法,有效避免了终端滑模面导致的奇异问题.最后,通过仿真验证了算法的有效性.

The fixed-time stabilization control for a class of second order nonlinear system subjected to unknown external disturbance is studied in this paper.First,a new fixed-time stabilization method is proposed,and the calculation of the convergence time and its upper bound estimation are given in details.Theoretical analysis shows that the upper bound of the convergence time can be totally determined by the system parameters independently on initial system states.Then,based on the proposed fixed-time stabilization method,a novel sliding mode reaching law and a novel terminal sliding mode surface are designed to make the system states first reaching to the sliding mode surface from any initial conditions and then converging to the original point along with the sliding mode surface in bounded finite-time,thus,the boundedness of the convergence time of the system states from anywhere to the original point is guaranteed.Meanwhile,the system state based auto switching method is employed to avoid the singular problem that caused by the terminal sliding mode surface.Finally,simulations are carried out to verify the effectiveness of the proposed method.