基于时域映射的多无人机系统给定时间分布式最优集结

针对多无人机系统给定时间最优集结问题，建立了基于时域映射的分布式优化框架。首先，引入一类特殊的时域映射，将原时域的给定时间决策问题转化为了无限域中的渐近稳定问题，简化了分析设计流程。其次，进一步设计了给定时间梯度下降算法，其收敛时间与系统初始条件及其他参数无关，能够被预先给定，且算法时变增益的使用消除了参数选择过程，在全局信息严重匮乏的情况下仍然适用。仿真结果表明:所提方法能够在给定时间内实现多无人机分布式最优集结，并保证任务时间内闭环系统全局有界。 

D istributed optimal rendezvous of multi-UAV systems in prescribed time based on time-domain mapping

To solve the prescribed-time optimal rendezvous problem for multi-UAV systems, a distributed optimization framework is established based on time-domain transformation technique. By introducing a specific time-domain transformation, the prescribed-time decision problem in original time-domain is transformed into an asymptotically stable problem in the infinite domain, which simplifies the analysis and design process. Then, we design a prescribed-time gradient descent algorithm whose convergence time is independent of the initial states as well as other parameters and therefore can be pre-specified. Besides, the application of time-varying gain removes the parameter selection process, which enables the proposed method in the context of a serious lack of global information. The simulation results show that this method is able to achieve the distributed optimal rendezvous for multiple UAVs in prescribed time, and the closed-loop system remains globally bounded in mission time.