非零势能的耗散力学控制系统的位形能控性  

Configuration Controllability for Non-Zero Potential Mechanical Control Systems With Dissipation

作　　者：康剑灵[1] 王红[2] 叶华文[3] 

机构地区：[1]东华大学应用数学系,上海200051 [2]南开大学数学科学院和核心数学与组合数学教育部重点实验室,天津300071 [3]西北工业大学自动控制系,西安710072

出　　处：《应用数学和力学》2005年第7期826-832,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10171081);2005年天津市自然科学基金资助

摘　　要：　在拉格朗日力学控制系统的仿射联络框架下,基于Sussmann对有限维流形上一般仿射非线性控制系统的能控性讨论,将简单力学控制系统短时间局部位形能控的一个可计算的充分条件推广到迷向耗散的系统上,并给出系统是平衡点能控的一个充分条件,其中,系统的拉格朗日函数为动能减势能·　在问题的讨论中,系统的能控李代数的向量场李括号运算,以及与系统位形流形的Levi_Civita联络相关的对称积起了重要作用·　尽管势能项会使系统的位形能控性讨论复杂化。Within the affine connection framework of Lagrangian control systems, based on the results of Sussmann on controllability of general affine control systems defined on a finite-dimensional manifold, a computable sufficient condition of configuration controllability for the simple mechanical control systems was extended to the case of systems with strictly dissipative energy terms of linear isotropic nature, and a sufficient condition of equilibrium controllability for the systems was also given, where Lagrangian is kinetic energy minus potential energy. Lie bracketting of vector fields in controllable Lie algebra, and the symmetric product associated with Levi-Civita connection show virtues in the discussion. Liouville vector field simplified the computation of controllable Lie algebra for the systems, although the terms of potential energy complicated the study of configuration controllability.

关 键 词：力学 能控性 仿射联络 对称积 迷向耗散 

分 类 号：O231[理学—运筹学与控制论]