Global robust finite time stabilization of a class of nonlinear uncertain systems
Global robust finite time stabilization of a class of nonlinear uncertain systems
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发表时间：
2011
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通讯作者：
Ma Jian-jun
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作者：
Ma Jian-jun
针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反馈镇定控制律.首先，针对标称系统设计了一种状态反馈控制律.利用李雅普诺夫直接法和LaSalle不变性原理，证明了所得到的闭环标称系统是全局渐近稳定的，且具有负齐次度.其次，引入一个辅助变量，利用有限时间收敛的二阶滑模超扭曲算法设计了补偿控制律，并利用有限时间李雅普诺夫函数确定了补偿控制律中参数的取值范围，最后，设计了一种连续反馈控制律，使闭环系统在有限时间内收敛到平衡点，仿真结果表明了所设计控制律的有效性。
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.