Abstract

A partially periodic control problem is considered, where the control parameter enters the initial condition. We study the formalization related to the calculus of variations. The necessary conditions are written out in the form of Euler–Lagrange equations, with the help of which an algorithm for finding the optimal program trajectories is developed. The results are illustrated by an example when the motion is described by a time-averaged hyperbolic equation at a sufficiently large well depth during a gas lift.

中文翻译：

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气举问题初始条件的优化控制

摘要

考虑部分周期性控制问题，其中控制参数进入初始条件。我们研究与变分法相关的形式化。必要的条件以欧拉-拉格朗日方程的形式写出，借助该方程，开发了寻找最佳程序轨迹的算法。通过一个例子说明了气举过程中在足够大的井深处用时间平均双曲方程描述运动时的结果。