标题： 控制仿射系统的最优控制几何 显示英文标题

标题： Geometry of Optimal Control for Control-Affine Systems

摘要： 受最优控制理论中控制仿射系统的普遍性启发，我们研究了在二维和三维情况下具有度量结构的点仿射控制系统的几何性质。 我们计算了具有度量结构的常型点仿射分布的局部等距不变量，针对具有2个状态和1个控制的系统以及具有3个状态和1个控制的系统，并使用庞特里亚金最大原理来寻找齐次示例的测地轨迹。 即使在这些低维情况下，这些系统的行为也出人意料地丰富和多样。 显示英文摘要

摘要： Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for point-affine distributions of constant type with metric structures for systems with 2 states and 1 control and systems with 3 states and 1 control, and use Pontryagin's maximum principle to find geodesic trajectories for homogeneous examples. Even in these low dimensions, the behavior of these systems is surprisingly rich and varied.