基于非光滑线性Lipschitz连续平面的滑模控制设计  

Sliding mode control design based on nonsmooth linear Lipschitz continuous surface

作　　者：霍鑫[1] 郑凯[1] 姚郁[1] 

机构地区：[1]哈尔滨工业大学控制与仿真中心,哈尔滨150080

出　　处：《控制与决策》2009年第11期1719-1722,1728,共5页Control and Decision

基　　金：国家自然科学基金项目(60674043)

摘　　要：利用Filippov解、Clarke广义梯度和非光滑Lyapunov稳定理论,对一类滑模面设计为非光滑线性Lipschitz连续平面的二阶系统滑模控制问题进行深入讨论.首先设计控制律,使闭环系统在有限时间内能够到达所设计的滑模面;然后证明系统在滑模面上的运动是渐近稳定的.放宽了对滑模控制中滑模面设计的要求,提高了所提出设计方法的灵活性,有利于改善系统性能.仿真结果验证了所提出设计方法的正确性和有效性.By utilizing the notion of Filippov solution, Clarke generalized gradient and nonsmooth Lyapunov stability theory, a further discuss on sliding mode control is presented for second-order systems with a nonsmooth linear Lipschitz continuous sliding surface. Firstly, a discontinuous control law is proposed, which drives the trajectories of the closed-loop system reaching the designed surface in finite time. Furthermore, in the framework of Filippov, the asymptotical stability of the trajectories on the linear Lipschitz continuous surface is proved. The sliding mode control is constructed for more general sense, which improves the performance of the closed-loop system. Finally, simulation result shows the effectiveness and correction of the designs.

关 键 词：Lipschitz连续平面 Filippov解 非光滑分析 Clarke广义梯度 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]