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文中研究了具有公式(3)表示的一般正积分泛函的最优控制系统的综合问题.在第一部分中研究了具有控制参数的一阶微分方程组.控制系统的终点状态为 n 维相空间内的某一逐段光滑边界的闭性区域Ω.文中指出了根据极大值原理和轨道终点的横截条件寻找引到Ω的所有最优轨迹的方法.这里详细地研究了具有二次泛函和被积函数中不明显含有控制参数的质量指标泛函的线性方程情况.在文中第二部分研究了等损耗区的主要特性.指出了等损耗区与最优控制函数之间的关系.导出了求算最优损耗函数 J(x)的偏微分方程,以及这一函数与最优控制函数 u(x)的关系.上述方法是我们曾在文献[5,6,7]中用过的最优快速系统的综合方法的推广.文章最后举有例证.
In this paper, we study the synthesis problem of the optimal control system with the general positive integral functional represented by formula (3). In the first part, we study the first order differential equations with control parameters.The end state of the control system is n-dimensional phase space The closed region of a certain smooth boundary in section Ω is pointed out.It is pointed out that we can find all the optimal trajectories leading to Ω according to the maximum principle and the end-point cross-section condition of the track.In this paper, In the second part of the paper, the main characteristics of equal loss region are studied, and the relationship between equal loss region and the optimal control function is pointed out. Derived the partial differential equation for calculating the optimal loss function J (x), and the relationship between this function and the optimal control function u (x). The above method was used in the literature [5,6,7] The promotion of an integrated method of optimal fast system.The article concludes with examples.