This paper investigates the multi-agent collision-free control problem for medium and large scale systems. For such multi-agent systems, it is the typical situation where conventional methods using either the usual centralized model predictive control (MPC), or even the distributed counterpart, would suffer from substantial difficulty in balancing optimality and computational efficiency. Additionally, the non-convex characteristics that invariably arise in such collision-free control and optimization problems render it difficult to effectively derive a reliable solution (and also to thoroughly analyze the associated convergence properties). To overcome these challenging issues, this work establishes a suitably novel parallel computation framework through an innovative mathematical problem formulation; and then with this framework and formulation, the alternating direction method of multipliers (ADMM) algorithm is presented to solve the sub-problems arising from the resulting parallel structure. Furthermore, an efficient and intuitive initialization procedure is developed to accelerate the optimization process, and the optimum is thus determined with significantly improved computational efficiency. As supported by rigorous proofs, the convergence of the proposed ADMM iterations for this non-convex optimization problem is analyzed and discussed in detail. Finally, a multi-agent system with a group of unmanned aerial vehicles (UAVs) serves as an illustrative example here to demonstrate the effectiveness and efficiency of the proposed approach.
翻译:本文调查了中大型系统多试剂无碰撞控制问题。对于这类多试剂系统来说,典型的情况是,使用通常的中央模型预测控制(MPC),甚至分布式对应方的常规方法在平衡最佳性和计算效率方面会遇到很大困难。此外,在这种无碰撞控制和优化问题中始终出现的非混凝土特性使得难以有效地找到可靠的解决办法(并深入分析相关的趋同特性)。为了克服这些具有挑战性的问题,这项工作通过创新数学问题的配方,建立了一个适当的新颖的平行计算框架;然后,在这个框架和配方中,提出了乘数算法的交替方向方法,以解决由此形成的平行结构所产生的次级问题。此外,还制定了高效和直观的初始化程序,以加速优化进程,从而确定最佳性,从而大大改进计算效率。在严格的证据的支持下,对拟议中的非凝聚问题统一式计算方法进行了详细分析和讨论;最后,一个多试管系统与一个拟议中的无人驾驶航空飞行器展示工具的系统一起展示了拟议航空飞行器的效能。