| 多项式非线性系统局部镇定控制 |
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| 引用本文： | 童长飞,章辉,孙优贤.多项式非线性系统局部镇定控制[J].控制与决策,2008,23(7). |
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| 作者姓名： | 童长飞 章辉 孙优贤 |
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| 作者单位： | 1. 浙江大学,工业控制技术国家重点实验室,杭州310027
2. 浙江大学,工业控制研究所,杭州310027 |
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| 基金项目： | 国家自然科学基金，浙江省科研项目 |
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| 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.
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| 关 键 词： | 非线性控制 半定规划松弛 局部镇定控制 |
Local stabilizing control for polynomial nonlinear systems |
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| TONG Chang-fei,ZHANG Hui,SUN You-xian.Local stabilizing control for polynomial nonlinear systems[J].Control and Decision,2008,23(7). |
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| Authors: | TONG Chang-fei ZHANG Hui SUN You-xian |
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| Affiliation: | TONG Chang-fei,ZHANG Hui,SUN You-xian (a.State Key Laboratory of Industrial Control Technology,b.Institute of Industrial Process Control,Zhejiang University,Hangzhou 310027,China.) |
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| Abstract: | 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 stabil... |
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| Keywords: | Nonlinear control Semidefinite programming relaxation Local stabilizing control |
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