具有零动态仿射非线性系统控制Lyapunov函数的构造  

Constructive control Lyapunov functions for affine nonlinear systems with zero dynamics

作　　者：蔡秀珊[1] 汪晓东[1] 吕干云[1] 

机构地区：[1]浙江师范大学数理与信息工程学院,浙江金华321004

出　　处：《控制理论与应用》2007年第3期391-395,共5页Control Theory & Applications

基　　金：浙江省自然科学基金资助项目(Y105141);浙江省教育厅科研基金资助项目(20050291);浙江师范大学国家基金预研资助项目(2005gjjj021).

摘　　要：研究具有零动态仿射非线性系统控制Lyapunov函数的构造问题.提出通过求解一个Lyapunov方程获得可线性化部分的二次型控制Lyapunov函数.由可线性部分的控制Lyapunov函数和零动态部分的Lyapunov函数,通过构造一个正定函数,得到了整个系统的控制Lyapunov函数,且设计了可半全局镇定整个闭环系统的控制律.仿真实例说明了所提出方法的有效性.The construction of control Lyapunov functions for affine nonlinear systems with zero dynamics is considered in this paper. A method is developed to ensure that a control Lyapunov function for the feedback linearizable part can be obtained by solving a Lyapunov equation. Using the control Lyapunov function of the feedback linearizable part and a Lyapunov function of the zero dynamics, a control Lyapunov function for the overall nonlinear system is then established by constructing a definite function. A state feedback is also designed to semiglobally stabilize the closed-loop system. Finally, a simulation example is given to illustrate the effectiveness of the design.

关 键 词：非线性系统 控制LYAPUNOV函数 半全局镇定 零动态 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]