作　　者： ; ; ;

机构地区： 东华大学理学院数学系

出　　处： 《工程数学学报》 2007年第1期138-144,共7页

摘　　要： 利用力学控制系统的仿射联络模型的内在几何齐次结构和李代数结构,研究了系统的短时间局部能控性,其中,系统的拉格朗日函数取为系统的动能。证明了单输入力学控制系统在零速度点是短时间局部能控的充分必要条件是系统位形流形的维数为1,并且将这一结论推广到迷向耗散的单输入力学控制系统上。 Relying on the inherent geometric homogeneous and Lie algebraic structure for the affine connection model of mechanical control systems with kinetic energy Lagrangian, the smalltime local controllability for the systems is explored. It is demonstrated that the system with a single-input is small-time locally controllable at the point and zero velocity if and only if the dimension of the configuration manifold is one. Furthermore, this result is extended to the case of single-input systems with isotropic damping. The controllability results for general affine control systems described by Sussmann provide impetus for the main results of the present paper.

关 键 词： 力学 仿射联络 能控性 齐次性 迷向耗散

领　　域： [理学] [理学]