最速控制系統的分析与綜合

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。

ANALYSIS AND SYNTHESIS OF TIME OPTIMAL CONTROL SYSTEMS

In this paper some new results concerning analysis and synthesis of time optimalcontrol systems are given. We assume that the motion of controlled object is describedby linear ordinary differential equations with variable coefficient, and the final states ofthe system form a convex region of phase space. Geometric properties of the iso-chronous region of these systems in phase space and the facts connected with these whichhavc fundamental meaning for the solution of the synthesis problem are discussed. More-over, the facts which are formulated in theorems have also their independent interest.At the end of this paper the method of synthesis of the optimal control system with con-stant and variable coefficients and two illustrative examples are given.