论文标题
飞机轨迹优化的奇异与边界弧线在攀爬阶段
Singular versus boundary arcs for aircraft trajectory optimization in climbing phase
论文作者
论文摘要
在本文中，我们对攀登阶段的最佳飞机轨迹感兴趣。我们考虑成本指数标准，这是攀登时间和燃油消耗的凸组合。我们假设推力是恒定的，并且我们控制飞机的飞行路径角。此优化问题被建模为具有控制中的单输入仿射动力学和两个纯状态约束的Mayer最佳控制问题，从而限制了校准的空速（CAS）和MACH速度。作为最小化的候选者作为最大原则给出的一组极端选择。我们首先分析了有关状态约束界限的最小攀爬时间问题，将较小的时间分析，间接多重拍摄和同型方法与监视结合在一起。这项调查强调了两种策略：航空学中的常见CAS/MACH程序和控制理论中经典的爆炸爆炸策略。然后，我们将这两个程序的成本指数标准比较。
In this article, we are interested in optimal aircraft trajectories in climbing phase. We consider the cost index criterion which is a convex combination of the time-to-climb and the fuel consumption. We assume that the thrust is constant and we control the flight path angle of the aircraft. This optimization problem is modeled as a Mayer optimal control problem with a single-input affine dynamics in the control and with two pure state constraints, limiting the Calibrated AirSpeed (CAS) and the Mach speed. The candidates as minimizers are selected among a set of extremals given by the maximum principle. We first analyze the minimum time-to-climb problem with respect to the bounds of the state constraints, combining small time analysis, indirect multiple shooting and homotopy methods with monitoring. This investigation emphasizes two strategies: the common CAS/Mach procedure in aeronautics and the classical Bang-Singular-Bang policy in control theory. We then compare these two procedures for the cost index criterion.
