基于交替方向乘子法的多智能体无碰撞模型预测控制并行优化
Alternating Direction Method of Multipliers-Based Parallel Optimization for Multi-Agent Collision-Free Model Predictive Control
AI总结：
针对多智能体无碰撞控制问题，提出基于ADMM的并行优化框架，解决非凸MPC难题，并通过高效初始化提升计算效率，仿真验证优于多种基线方法。
摘要：
本文研究了多智能体系统的无碰撞控制问题。对于此类多智能体系统，通常采用传统的集中式模型预测控制（MPC）甚至分布式模型预测控制的方法，在平衡最优性和计算效率方面会遇到很大困难。此外，此类无碰撞控制和优化问题中不可避免地出现的非凸特性，使得难以有效获得可靠的解（以及彻底分析相关的收敛性质）。为了克服这些具有挑战性的问题，本工作通过创新的数学问题表述建立了一个适当新颖的并行计算框架；然后在此框架和表述的基础上，提出了一种基于交替方向乘子法（ADMM）的并行算法来求解由此产生的并行结构中的子问题。此外，开发了一种高效且直观的初始化程序以加速优化过程，从而以显著提高的计算效率确定最优解。在严格证明的支持下，针对该非凸优化问题所提出的ADMM迭代的收敛性得到了详细分析和讨论。最后，以一组无人机（UAV）的仿真作为示例，展示了所提出方法的有效性和效率。同时，仿真结果验证了与其他基线方法（包括原始二次混合整数规划（PQ-MIP）、非凸二次混合整数规划（NC-MIP）和非凸二次约束二次规划（NC-QCQP））相比，在精度和计算效率方面的显著改进。
英文摘要：
This paper investigates the collision-free control problem for multi-agent 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, a parallel algorithm based on alternating direction method of multipliers (ADMM) 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 simulation with a group of unmanned aerial vehicles (UAVs) serves as an illustrative example here to demonstrate the effectiveness and efficiency of the proposed approach. Also, the simulation results verify significant improvements in accuracy and computational efficiency compared to other baselines, including primal quadratic mixed integer programming (PQ-MIP), non-convex quadratic mixed integer programming (NC-MIP), and non-convex quadratically constrained quadratic programming (NC-QCQP).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
