发表机构
University of California, Irvine; Iowa State University（加州大学尔湾分校; 爱荷华州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于均值场近似的控制框架，将多目的地UAM网络路由建模为CTMC并证明无排队状态的正不变性，从而将无限维最优控制问题转化为有限维代数优化，实现安全无拥塞运行。
AI 中文摘要
随着城市空中交通（UAM）系统向高密度运行规模发展，管理自主无人驾驶飞行器（UAV）交通需要既易于处理又具有安全关键性的控制框架。本文为受垂直起降场容量和流量约束的多目的地UAM网络中的路由问题，提出了一个基于最优控制理论的原理性基础。我们首先将网络建模为目的地条件下的连续时间马尔可夫链（CTMC），以捕捉排队、服务和飞行状态之间的随机转移。为确保可处理性，我们采用均值场流体近似，并将底层系统动力学推导为一组耦合的常微分方程。本工作的一项关键贡献是正式证明了无排队状态空间的正不变性。我们证明，在特定的欠载条件下，初始无排队的系统将无限期保持无排队状态。这一结果使我们能够将复杂的无限维连续时间最优控制问题转化为可处理的有限维代数优化问题。所提出的框架在确保网络范围稳定性的同时，联合优化了旅行时间和多跳效率。我们通过刻画稳态流量均衡并为大规模移动系统中的安全、无拥塞运行提供充分条件来验证该方法。
英文摘要
As Urban Air Mobility (UAM) systems scale toward high-density operations, managing autonomous Unmanned Aerial Vehicle (UAV) traffic requires control frameworks that are both tractable and safety-critical. This paper presents a principled optimal control-theoretic foundation for routing in multi-destination UAM networks subject to vertiport capacity and flow constraints. We first model the network as a destination-conditioned Continuous-Time Markov Chain (CTMC) to capture the stochastic transitions between queueing, service, and flight states. To ensure tractability, we employ a mean-field fluid approximation and derive the underlying system dynamics as a set of coupled ordinary differential equations. A key contribution of this work is the formal proof of the positive invariance of the queue-free state space. We demonstrate that under specific underloaded conditions, a system initialized without queues will remain queue-free indefinitely. This result allows us to transform a complex, infinite-dimensional continuous-time optimal control problem into a tractable, finite-dimensional algebraic optimization. The resulting framework jointly optimizes for travel time and multi-hop efficiency while ensuring network-wide stability. We validate the approach by characterizing the steady-state flow equilibria and providing sufficient conditions for safe, congestion-free operation in large-scale mobility systems.
