The linear time-optimal problem for some classes of linear systems with a multidimensional control is considered. The general position condition, which guarantees the uniqueness of the optimal control, is not assumed to be satisfied. We introduce a vector moment min-problem, which is a further development of the moment min-problem proposed by V.I. Korobov and G.M. Sklyar in 1987 for solving linear time-optimal problems with a one-dimensional control. In the paper the case of the time-optimal problem for linear systems with two-dimensional control is thoroughly studied by use of the vector moment min-problem.

中文翻译：

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具有多维控制和向量矩最小问题的系统的时间最优性

考虑了某些具有多维控制的线性系统的线性时间最优问题。不能保证保证最佳控制唯一性的一般位置条件。我们介绍了矢量矩最小问题，它是VI Korobov和GM Sklyar于1987年提出的矩最小问题的进一步发展，用于用一维控制解决线性时间最优问题。在本文中，利用矢量矩最小问题对带有二维控制的线性系统的时间最优问题进行了深入研究。