We consider a nonlinear control system in Euclidean space on a finite time interval with controls subject to geometric constraints. The question of constructing lower and upper (by inclusion) approximations of reachable sets of this system is studied. Under certain conditions, estimates are obtained for the discrepancy (in the Hausdorff metric) between the lower and upper approximations of the reachable sets.

中文翻译：

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具有几何约束的控制系统可达集的两侧逼近

我们在有限时间间隔上考虑欧几里得空间中的非线性控制系统，其控制受几何约束。研究了构建该系统可达集的下和上（通过包含）近似的问题。在某些条件下，会获得可达集的下近似值和上近似值之间的差异（在 Hausdorff 度量中）的估计值。