Abstract

The problem of the speed of performance (speed, performance) of a group of controlled objects is considered, the initial state of each of which is given, and the final state is selected from a fixed set of possible terminal states (targets). For each object, it is required to assign a target and find the control that ensures that the group simultaneously reaches all the selected targets in the shortest time. Since the speed-optimal controls of individual objects do not solve the problem of group speed, the so-called minimally delayed trajectories are used. A technique for solving the problem is developed, which includes an algorithm for solving the minimax assignment problem and a procedure for using the optimal and minimally delayed trajectories. The problem of the speed of a group of objects, whose planar motion is represented by Markov–Dubins trajectories, is solved.

中文翻译：

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一组受控对象的执行速度

摘要

考虑一组受控对象执行速度（速度、性能）的问题，给定每个受控对象的初始状态，并从一组固定的可能终止状态（目标）中选择最终状态。对于每个对象，需要分配一个目标并找到保证该组在最短的时间内同时达到所有选定目标的控制。由于单个对象的速度最优控制不能解决群体速度的问题，因此使用所谓的最小延迟轨迹。开发了一种解决该问题的技术，其中包括解决极小极大分配问题的算法以及使用最优和最小延迟轨迹的过程。解决了一组物体的速度问题，其平面运动由马尔可夫-杜宾斯轨迹表示。