垂直起降飞机非线性动态调度问题的分段线性值函数逼近
Piecewise linear value function approximations in nonlinear dynamic scheduling problems with VTOLs
摘要：
现代垂直起降飞行器（VTOL）可能会对未来的机动性产生重大影响。其广泛的应用领域包括城市空中机动、运输和后勤以及军事背景下的侦察和观察任务。本文提出了一个有效的数值框架，多个垂直起降飞机的动态调度。它将调度问题与最优轨迹规划相结合。整个整定过程可归结为一个混合整数双层最优化问题。在上层，安排垂直起降，并计算其开始时间。较低层次问题的解决方案涉及到一个值函数的计算，并为每个飞行器产生最佳轨迹。为了解决两层问题，将其转化为单层问题。然后将得到的混合整数非线性规划（MINLP）分段线性化，并采用基于分支定界算法的线性求解器进行数值求解。数值结果证明了本文方法的可行性。
英文摘要：
Modern vertical take-off and landing vehicles (VTOLs) could significantly affect the future of mobility. The broad range of their application fields encompasses urban air mobility, transportation and logistics as well as reconnaissance and observation missions in a military context. This article presents an efficient numerical framework for dynamic scheduling of multiple VTOLs. It combines a scheduling problem with optimal trajectory planning. The whole setting is formulated as a mixed-integer bilevel optimization problem. At the upper level, VTOLs are scheduled, and their starting times are computed. The solution of the lower level problem involves the computation of a value function and yields optimal trajectories for every aerial vehicle. In order to solve the bilevel problem,it is recast into a single-level one. The resulting mixed-integer nonlinear program (MINLP) is then piecewise linearized and solved numerically by a linear solver based on the Branch-and-Bound algorithm. Numerical results prove the feasibility of the approach proposed in this work.
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