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本文介绍一些关于最速系统的分析与综合理论的新结果。受控系统的运动设为变系数线性常微分方程组所描述,而系统的终点状态是相空间内的某一凸性区域。文内详细介绍了相空间内等时区的几何特性及与此有关的事实,它们对系统综合具有重要意义。此外,以定理形式所叙述的事实具有独立的意义。文末指出线性变系数和常系数系统的综合方法及应用这一方法的例题。
This article presents some new results on the analysis and synthesis of the steepest systems. The motion of the controlled system is set as the system of variable linear ordinary differential equations, and the end state of the system is a convex region in the phase space. The text details the geometric properties of the isochrones in the phase space and the facts related to them, which are important for system synthesis. In addition, the facts described in the form of a theorem have independent meanings. At the end of this article, we point out the synthesis method of linear variable coefficient and constant coefficient system and the example of applying this method.