SIAM Journal on Control and Optimization, Volume 59, Issue 1, Page 320-338, January 2021.
The aim of this paper is to generalize some ideas related to the concept of causality in General Relativity and to carry them over to the theory of control systems. Suppose that $M$ is a smooth manifold, and let $(\Sigma)\;\dot{q}=f_u(q), u\in\mathcal{U}$, be a control system on $M$ satisfying certain natural conditions. It is proved that if $F\colon M\longrightarrow M$ is a bijection such that $F$ and $F^{-1}$ map the trajectories of $(\Sigma)$ onto trajectories of $(\Sigma)$, then $F$ is a homeomorphism.

中文翻译：

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因果关系和控制系统

SIAM控制与优化杂志，第59卷，第1期，第320-338页，2021
年1月。本文的目的是概括一些与广义相对论因果关系概念有关的思想，并将其推广到控制理论中系统。假设$ M $是一个平滑流形，并且让$（\ Sigma）\; \ dot {q} = f_u（q），u \ in \ mathcal {U} $是一个满足$ M $的控制系统自然条件。证明如果$ F \冒号M \ longrightarrow M $是双射，使得$ F $和$ F ^ {-1} $将$（\ Sigma）$的轨迹映射到$（\ Sigma）$的轨迹，则$ F $是同胚。