为解决给定时间的多无人机（unmanned aerial vehicles, UAVs）最优集结问题，通过分布式优化的方法研究能够使多无人机在权重不平衡有向通信网络下按照给定时间范围内完成最优集结的控制算法。每架无人机都有其相应的局部目标函数，全局目标函数就是每架无人机所具有的局部目标函数之和，算法的目的就是通过分布式控制的方式，找到满足全局目标函数的最优集结点，采用时域映射的思想，将原本的给定时间下的集结问题转变为无限时域下的集结问题，并通过拉普拉斯零特征值下的左特征向量克服权重不均衡有向网络的不平衡性。结合凸分析理论和李雅普诺夫稳定性理论，验证了算法能够收敛到最优的解。仿真结果表明：不同出发点的无人机，在算法的控制下，均可以在给定时间内到达最优的集结点。

To address the problem of optimal rendezvous for multiple unmanned aerial vehicles (UAVs) within a given time frame, a distributed optimization approach was investigated for developing a control algorithm that enabled UAVs to achieve optimal rendezvous in a directed communication network with unbalanced weights. Each UAV was associated with a local objective function, and the global objective function was defined as the sum of the local objective functions of all UAVs. The aim of the algorithm was to find the optimal rendezvous point that satisfies the global objective function through distributed control. Inspired by the concept of temporal mapping, the given time-constrained rendezvous problem was transformed into an unconstrained rendezvous problem in infinite time domain, overcoming the imbalance in the directed network by utilizing the left eigenvectors corresponding to the zero eigenvalue of the Laplacian matrix. By combining convex analysis theory and Lyapunov stability theory, the algorithm's convergence to the optimal solution was validated. Simulation results demonstrate that UAVs with different initial positions can reach the optimal rendezvous point within the given time frame under the control of the proposed algorithm.