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本文引用格式:章婷婷,张毅,张成璞,陈向炜.判定定常Chetaev型非完整系统稳定性的三重组合梯度方法[J].动力学与控制学报,2019,17(4):306~312;   Zhang Tingting,Zhang Yi,Zhang Chengpu,Chen Xiangwei.Triple combined gradient method for judging the stability of nonholonomic systems of constant Chetaev′s type[J].Journal of Dynamics and Control,2019,17(4):306-312.
判定定常Chetaev型非完整系统稳定性的三重组合梯度方法    点此下载全文
章婷婷  张毅  张成璞  陈向炜
苏州科技大学 数理学院, 苏州 215009,苏州科技大学 土木工程学院, 苏州 215011,商丘师范学院 电子电气工程学院, 商丘 476000,商丘师范学院 物理与电气信息学院, 商丘 476000
基金项目:国家自然科学基金资助项目(11372169,11272227,11572212)
DOI:10.6052/1672-6553-2019-025
摘要:
      研究判定定常Chetaev型非完整系统稳定性的三重组合梯度方法. 首先,分别给出4类基本梯度系统和4类三重组合梯度系统的定义和微分方程;其次,得到非完整系统的相应完整系统成为三重组合梯度系统的条件,从而将定常Chetaev型非完整系统化成各类三重组合梯度系统;最后,利用三重组合梯度系统的性质来研究系统的稳定性. 举例说明结果的应用.
关键词:非完整系统,三重组合梯度系统,稳定性
Triple combined gradient method for judging the stability of nonholonomic systems of constant Chetaev′s type    Download Fulltext
Zhang Tingting  Zhang Yi  Zhang Chengpu  Chen Xiangwei
Fund Project:
Abstract:
      A triple combined gradient method was studied to determine the stability of nonholonomic systems of constant Chetaev′s type. Firstly,the definitions and differential equations of four classes of basic gradient systems and four classes of triple combined gradient systems were given. Secondly,the conditions,under which the corresponding holonomic systems of nonholonomic systems become triple combined gradient systems,were obtained. Therefore,the constant Chetaev nonholonomic systems can be transformed into various triple combined gradient systems. Finally,the stability of the system is studied by using the properties of the triple combined gradient system. The applications of this method were illustrated by four examples.
Keywords:nonholonomic systems,triple combined gradient method,stability
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