零曲率的控制系统不一定是可忽略的
Control systems of zero curvature are not necessarily trivializable
摘要：
一个控制系统$\dot{q} = f(q,u)$被称为可平凡化的，如果存在局部坐标系，在该坐标系中，系统被反馈等价于形式为$\dot{q} = f(u)$的控制系统。本文刻划了可平凡化的控制系统和在反馈变换下$f$与$\partial f/\partial u$可交换的控制系统。特征给出的反馈不变量的系统（其控制曲率和中心的仿射曲率），因此是完全内在的。最后，我们将所得结果应用于黎曼流形上的Zermelo问题。
英文摘要：
A control system $\dot{q} = f(q,u)$ is said to be trivializable if there exists local coordinates in which the system is feedback equivalent to a control system of the form $\dot{q} = f(u)$. In this paper we characterize trivializable control systems and control systems for which, up to a feedback transformation, $f$ and $\partial f/\partial u$ commute. Characterizations are given in terms of feedback invariants of the system (its control curvature and its centro-affine curvature) and thus are completely intrinsic. To conclude we apply the obtained results to Zermelo-like problems on Riemannian manifolds.
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