首先从整体化的观点定义了一种建立在三维欧氏空间的二维曲面上的非线性控制系统,并给出了在曲面的局部坐标系下非线性系统状态方程的表达式,研究了非线性系统的平衡态与曲面的测地线之间的关系.刻划了球面、柱面、锥面的特殊曲面几何结构和奇异结构与非线性控制系统之间的内在联系.进一步,讨论了建立在球面、柱面和锥面上的非线性控制系统的局部和整体能控性与能观测性.

In this paper,from the global viewpoint we first efine the nonlinear control system on a two dimensional surface in the three dimensional Euclidean space,give the representation of the state equation under a local coordinate system of the surface,and study the connection between the equilbrium state of the nonlinear system and the geodesics on the surface.Secondly,we show the intimate relation between the nonlinear control system and the special geometrical structure and singular structure of a sphere,a cylindroid and a cone.Moreover,we discuss the local and global controllability and observability of the nonlinear system on the sphere,the cylindroid and the cone.