In this article, the formation mission design problem for commercial aircraft is studied. Given the departure times and the departure and arrival locations of several commercial flights, the relevant weather forecast, and the expected fuel savings during formation flight, the problem consists in establishing how to organize them in formation or solo flights and in finding the trajectories that minimize the overall direct operating cost of the flights. Each aircraft can fly solo or in different positions inside a formation. Therefore, the mission is modeled as a switched dynamical system, in which the discrete state describes the combination of flight modes of the individual aircraft and logical constraints in disjunctive form establish the switching logic among the discrete states of the system. The formation mission design problem has been formulated as an optimal control problem of a switched dynamical system and solved using an embedding approach, which allows switching decision among discrete states to be modeled without relying on binary variables. The resulting problem is a classical optimal control problem which has been solved using a knotting pseudospectral method. Several numerical experiments have been conducted to demonstrate the effectiveness of this approach. The obtained results show that formation flight has great potential to reduce fuel consumption and emissions.

中文翻译：

---

基于切换优化控制技术的商用飞机编队任务设计

本文研究了商用飞机编队任务设计问题。考虑到几个商业航班的起飞时间和起飞和到达位置、相关的天气预报以及编队飞行期间预期的燃油节省，问题在于确定如何在编队或单飞中组织它们，并找到最小化的轨迹航班的整体直接运营成本。每架飞机都可以单独飞行或在编队内的不同位置飞行。因此，任务被建模为一个切换动力系统，其中离散状态描述了单个飞机的飞行模式的组合，并以分离形式的逻辑约束建立了系统离散状态之间的切换逻辑。编队任务设计问题已被表述为切换动力系统的最优控制问题，并使用嵌入方法解决，该方法允许在不依赖二元变量的情况下对离散状态之间的切换决策进行建模。由此产生的问题是一个经典的最优控制问题，已使用打结伪谱方法解决。已经进行了几个数值实验来证明这种方法的有效性。所得结果表明，编队飞行在降低油耗和排放方面具有巨大潜力。由此产生的问题是一个经典的最优控制问题，已使用打结伪谱方法解决。已经进行了几个数值实验来证明这种方法的有效性。所得结果表明，编队飞行在降低油耗和排放方面具有巨大潜力。由此产生的问题是一个经典的最优控制问题，已使用打结伪谱方法解决。已经进行了几个数值实验来证明这种方法的有效性。所得结果表明，编队飞行在降低油耗和排放方面具有巨大潜力。