A fixed-time package guidance problem is considered for a linear controlled dynamic system with a finite set of initial states. The control set is convex and compact and the target set is convex and closed. The paper focuses on the case where the set of initial states has singular clusters for which the existing algorithm for estimating the elements of a guiding program package is not applicable. It is suggested to consider a perturbed problem of extended program guidance with a smoothed control set. It is proved that the motions of the original and perturbed problems are close to each other at the terminal time; the corresponding estimates are provided. In the case of an extended target set with nonempty interior, it is also shown that a solution of the extended program guidance problem that is precisely guiding to the target set can be obtained by applying the existing algorithm for the perturbed problem with compressed target set. The suggested theoretical constructions are illustrated with a model example.

中文翻译：

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包制导问题中一组初始状态奇异簇的制导程序包要素的计算

对于具有有限初始状态集的线性受控动态系统，考虑了固定时间的包装制导问题。控制集是凸且紧凑的，目标集是凸且闭合的。本文着重于初始状态集具有奇异簇的情况，对于该簇而言，现有的估计指导程序包元素的算法不适用。建议考虑具有平滑控制集的扩展程序指南的扰动问题。事实证明，原始问题和扰动问题的运动在结束时彼此接近。提供了相应的估计。对于带有非空内部空间的扩展目标，还表明，可以通过将现有算法用于压缩目标集的摄动问题，来获得精确地引导至目标集的扩展节目指导问题的解决方案。建议的理论构造通过模型示例进行说明。