In this paper which is closely related to the previous paper [3] we specify general theory developed there. We study the structure of Jacobi fields in the case of an analytic system and piecewise analytic control. Moreover, we consider only 1-dimensional control variations. Jacobi fields are piecewise analytic in this case but may have jump discontinuities. We derive ODEs that these fields satisfy on the intervals of regularity and study behavior of the fields in a neighbourhood of a singularity where the ODE becomes singular and the Jacobi fields may have jumps.

中文翻译：

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最优控制中的Jacobi场：一维变化

在与前一篇论文[3]密切相关的本文中，我们指定了在那里发展的一般理论。我们在解析系统和分段解析控制的情况下研究了Jacobi场的结构。此外，我们仅考虑一维控制变量。Jacobi字段在这种情况下是分段分析的，但可能具有跳跃间断。我们推导了这些场在规则性间隔上满足的ODE，并研究了在ODE变得奇异且Jacobi场可能跳跃的奇点附近的场行为。