商用飞机编队任务设计的随机切换最优控制方法
A Stochastic Switched Optimal Control Approach to Formation Mission Design for Commercial Aircraft
AI总结：
针对离场时间和编队节油不确定性下的商用飞机编队任务设计，本文提出随机切换最优控制建模与非侵入式广义多项式混沌随机配置求解方法，证明编队仍可降低期望直接运营成本。
摘要：
本文研究了在存在不确定性的情况下商用飞机的编队任务设计问题。具体而言，本文考虑了飞机离场时间以及尾随飞机燃油消耗节省量方面的不确定性。给定若干商用航班，该问题在于将它们安排为编队飞行或单独飞行，并寻找使航班直接运营成本期望值最小化的轨迹。编队任务设计问题被表述为一个随机切换动力系统的最优控制问题，并采用基于非侵入式广义多项式混沌的随机配置法求解。该随机配置方法将随机切换最优控制问题转化为一个增广的确定性切换最优控制问题。通过这种方法，使用少量随机参数采样点来联合求解切换最优控制问题的特定实例。随后，利用这些采样点，将所得解表示为关于随机参数的正交多项式展开。该技术能够以较低的计算成本对随机解进行统计分析和全局灵敏度分析。本研究旨在确定在存在不确定性的情况下，就直接运营成本的期望值而言，编队任务相对于单独飞行是否有利。本文开展了若干数值实验，其中考虑了离场时间以及编队飞行期间燃油节省量的不确定性。所得结果表明，即使在存在这些不确定性的情况下，也能够实现收益。
英文摘要：
This paper studies the formation mission design problem for commercial aircraft in the presence of uncertainties. Specifically, it considers uncertainties in the departure times of the aircraft and in the fuel burn savings for the trailing aircraft. Given several commercial flights, the problem consists in arranging them in formation or solo flights and finding the trajectories that minimize the expected value of the direct operating cost of the flights. The formation mission design problem is formulated as an optimal control problem of a stochastic switched dynamical system and solved using nonintrusive generalized polynomial chaos based stochastic collocation. The stochastic collocation method converts the stochastic switched optimal control problem into an augmented deterministic switched optimal control problem. With this approach, a small number of sample points of the random parameters are used to jointly solve particular instances of the switched optimal control problem. The obtained solutions are then expressed as orthogonal polynomial expansions in terms of the random parameters using these sample points. This technique allows statistical and global sensitivity analysis of the stochastic solutions to be conducted at a low computational cost. The aim of this study is to establish if, in the presence of uncertainties, a formation mission is beneficial with respect to solo flight in terms of the expected value of the direct operating costs. Several numerical experiments have been conducted in which uncertainties on the departure times and on the fuel saving during formation flight have been considered. The obtained results demonstrate that benefits can be achieved even in the presence of these uncertainties.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
