Singular versus boundary arcs for aircraft trajectory optimization in climbing phase

IF 1.9 3区数学 Q2 Mathematics

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2022-12-13 DOI:10.1051/m2an/2022101

O. Cots, J. Gergaud, D. Goubinat, B. Wembe

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引用次数: 1

Abstract

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 air slope 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.

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爬升阶段飞机轨迹优化的奇异弧与边界弧

在本文中，我们感兴趣的是飞机爬升阶段的最优轨迹。考虑了爬升时间和燃油消耗的凸组合成本指标准则。我们假设推力是恒定的，我们控制飞机的气流斜率。该优化问题被建模为一个Mayer最优控制问题，在控制中具有单输入仿射动力学，并具有两个纯状态约束，限制了校准空速(CAS)和马赫速度。作为最小值的候选者是从由极大值原理给出的一组极值中选出的。我们首先结合小时间分析、间接多次射击和同伦方法与监测相结合，根据状态约束的边界分析了最小爬升时间问题。本文着重研究了两种策略:航空学中常用的CAS/Mach程序和控制理论中经典的bang - singularity - bang策略。然后，我们比较这两种程序的成本指数标准。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique 数学-应用数学

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

6-12 weeks

期刊介绍： M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.