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Optimal Controlled Descent in the Atmosphere and the Modified Brachistochrone Problem ?

机译：在大气中最佳控制下降和修改的Brachistochrone问题 ？

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摘要

The problem of maximization of the horizontal coordinate and minimization of the fuel expenditures of mass-point moving in the vertical plane driven by gravity, linear and quadratic viscous drag, and thrust is considered. The slope angle and the thrust are considered as a control variables. The problem is related to the modified brachistochrone problem. Principle maximum procedure allows to reduce the optimal control problem to the boundary value problem for a set of systems of two nonlinear differential equations. Thrust control depending on the velocity and slope angle is designed. It is established that the extreme thrust control program consists either of single arc with intermediate thrust control, or two arcs, starting with maximum thrust and ending with the intermediate thrust or three arcs: ”intermediate-maximum-intermediate”.
机译：考虑了在由重力，线性和二次粘性阻力驱动的垂直平面中移动的水平坐标和燃料消耗的水平坐标和最小化的问题。斜角和推力被认为是控制变量。问题与修改后的Brachistochrone问题有关。原理最大过程允许将最佳控制问题降低到两个非线性微分方程的一组系统的边值问题。设计了根据速度和斜坡角度的推力控制。建立极端推力控制程序由中间推力控制的单个弧或两个弧形组成，从最大推力开始并以中间推力或三个弧结束：“中间最大中间”。

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