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Computer Generation of Lyapunov Functions and Its Applications

Lyapunov函数的计算机生成及其应用

基本信息

批准号：
05650371
负责人：
HANEDA Hiromasa
金额：
$ 1.22万
依托单位：
Kobe University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1993
资助国家：
日本
起止时间：
1993 至 1994
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05650371/
关键词：
Lyapunov Functions Nonlinear Systems Estimate of Stability Regions Computer Generation of Lyapunov Functions Genelarization of Sector Condition Dynamic Convex Hull Algorithm Variable Structure Control System リヤプノフ関数の自動生成安定解析計算機による自動生成

项目摘要

1. Algorithm for lmproving polytope lyapunov Function : We examined several method to improve polytope Lyapunov functions, and we conclude that the most useful method is that adding vectors which are extreme points of vector field generated by the generalized sector conditions to the present polytope. Moreover, by using real Jordan canonical form, we proposed a method to generate useful an initial polytope.2. Dynamic Convex Hull Algorithm : We proposed a new dynamic convex hull algorithm which requires less memories and computing time than the Beneath-Beyond method.3. Discontinuous Systems : We derived a stability result for discontinuous systems which may have sliding modes. The result is almost same with that for continuous systems. Moreover, by using a polytope Lyapunov function, we proposed a design method for variable structure control systems. This method can eliminate chattering.4. Applications : We applied the polytope Lyapunov function to the stability analysis of composite systems. We also applied it to the stability analysis of fussy control systems, and showed that, by applying generalized sector conditions, we can guarantee the stability with less conservative conditions than the traditional Lyapunov functions such as quadratic Lyapunov functions and so on.

1.多胞型李雅普诺夫函数的改进算法：本文研究了几种改进多胞型李雅普诺夫函数的方法，认为最有效的方法是在现有多胞型上增加由广义扇形条件生成的向量场的极值点向量。此外，利用真实的Jordan标准形，提出了一种生成有用的初始多面体的方法.动态凸船体算法：提出了一种新的动态凸船体算法，该算法比Beneath-Beyond方法需要更少的内存和计算时间.不连续系统：我们推导出一个稳定性结果的不连续系统，可能有滑动模式。其结果与连续系统的结果基本相同。利用多胞型李雅普诺夫函数，提出了一种变结构控制系统的设计方法。这种方法可以消除抖动.应用：将多胞型李雅普诺夫函数应用于组合系统的稳定性分析。我们还将其应用于模糊控制系统的稳定性分析，并证明了通过应用广义扇区条件，我们可以保证稳定性的保守性条件比传统的李雅普诺夫函数，如二次李雅普诺夫函数等更少。