Establishment of nonlinear control theory taking into account global structure of manifold

本文提出了一种控制一般流形（包括非欧几里德空间）上非线性系统的一般框架，这是以往控制理论无法处理的。卫星的全球姿态控制、车辆的避障和机器人的控制都是我们问题的例子。该框架提供了自动生成具有不连续、逻辑或随机性的控制律的设计过程，这些控制律的性质对于在非欧几里德空间上稳定此类系统是必要的。

This study presents a general framework for controlling nonlinear systems on general manifolds including non-Euclidean spaces which precedent control theories cannot handle. Global attitude control of satellites, obstacle avoidance of vehicles, and control of acrobots are examples of our problem. This framework provides design procedures generating control laws automatically with discontinuity, logic, or randomness, of which properties are necessary to stabilize such systems on non-Euclidean spaces.