一类不确定非线性系统的全局鲁棒有限时间镇定

Global robust finite time stabilization of a class of nonlinear uncertain systems

对一类不确定非线性系统提出了一种连续的全局鲁棒有限时间控制律.首先,针对标称系统设计出了一种状态反馈控制律,应用Lyapunov直接稳定性理论和LaSalle不变性原理证明了闭环标称系统的全局渐近稳定性,同时具有负的齐次度,其次,引入辅助变量和采用有限时间收敛的二阶滑模Super-twisting算法,设计出了对不确定性和干扰进行抑制的补偿控制项,并根据有限时间Lyapunov函数给出了补偿控制项参数的取值范围;最后,综合得到一种连续的使实际闭环系统有限时间收敛到平衡点的鲁棒镇定控制律.仿真结果表明了所提控制律的有效性.

A continuous global robust finite time feedback stabilization control law is proposed for a class of uncertain nonlinear systems. Firstly, a state feedback control law is designed for the nominal system. By using Lyapunov direct method and LaSalle invariance principle, we prove that the resulting closed-loop nominal system is globally asymptotically stable with the negative homogeneity in degrees. Secondly, introducing an auxiliary variable, we design a compensated control law for compensating the uncertainties of the system by using the finite-time convergent second-order sliding mode Super-twisting algorithm. The range of the parameters in the compensation control law is determined by using the finite- time Lyapunov function. Finally, a continuous feedback control law is developed for the closed-loop system to converge to its equilibrium point in a finite period of time. Simulation results show the effectiveness of the proposed control law.