多项式非线性系统局部镇定控制  

Local stabilizing control for polynomial nonlinear systems

作　　者：童长飞[1] 章辉[1] 孙优贤[1] 

机构地区：[1]浙江大学工业控制技术国家重点实验室,工业控制研究所杭州310027

出　　处：《控制与决策》2008年第7期786-790,共5页Control and Decision

基　　金：国家自然科学基金项目(60674028,60736021);浙江省重大科技计划项目(2006C11066)

摘　　要：针对多项式非线性系统,提出一种用于验证二次型候选Lyapunov函数的数值计算方法.在该方法中,多项式系数被分解成带自由变量的系数矩阵,将正定性验证问题转化为矩阵不等式问题求解.对于局部稳定性分析,采用多个Lyapunov函数来趋近吸引域.每个Lyapunov函数均在各指定方向上进行最大半径优化.在稳定性分析基础上,提出保收敛率的局部镇定控制器设计方法以扩大吸引域.A numerical solution method is proposed to verify quadratic Lyapunov function candidate for polynomial nonlinear systems. In the method, the coefficients of a polynomial are decomposed to a matrix with free variables, and positivity validation is checked by solving derived matrix inequalities. For local stability analysis, multi-Lyapunov- functions are considered to approximate the domain of attraction. Each Lyapunov function is optimized with maximum radius at every specified direction. Based on the work of stability analysis, a local stabilizing control scheme ＇with guaranteed convergence rate is addressed to expend the domain of attraction.

关 键 词：非线性控制 半定规划松弛 局部镇定控制 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]