面向集群的可扩展鲁棒优化：一种分布式视角
Scaling Robust Optimization for Swarms: A Distributed Perspective
AI总结：
本文提出一种基于ADMM的分布式鲁棒优化框架，通过鲁棒重构、机会约束和分布引导技术，在保证安全的前提下实现多达246个智能体在非凸环境中的可扩展控制。
摘要：
本文介绍了一种用于不确定性条件下安全多智能体控制的分布式鲁棒优化框架。尽管随机噪声一直是此类系统中建模不确定性的主要形式，但这些表述在应对本质上具有确定性或缺乏概率数据的不确定性时可能力不从心。为确保此类场景下的安全性，我们采用鲁棒约束的概念，这些约束必须对有界集合内所有可能的不确定性实现均成立。然而，由于安全多智能体控制中涉及约束数量庞大或非凸性，标准鲁棒优化方法变得难以求解。为此，我们引入了新颖的鲁棒重构方法，在不牺牲安全性的前提下显著降低复杂度。通过纳入鲁棒机会约束和分布引导技术，该框架的适用性进一步扩展，可同时处理确定性不确定性和随机不确定性。为实现可扩展性，我们基于交替方向乘子法（ADMM）推导出一种分布式方法，并辅以考虑底层非凸性的收敛性研究。此外，我们还给出了计算复杂度界，突出所提框架相对于标准方法的效率优势。最后，通过涵盖非凸障碍物环境及多达246个智能体的多种场景的大量仿真结果，验证了该框架的鲁棒性和可扩展性。
英文摘要：
This article introduces a decentralized robust optimization framework for safe multi-agent control under uncertainty. Although stochastic noise has been the primary form of modeling uncertainty in such systems, these formulations might fall short in addressing uncertainties that are deterministic in nature or simply lack probabilistic data. To ensure safety under such scenarios, we employ the concept of robust constraints that must hold for all possible uncertainty realizations lying inside a bounded set. Nevertheless, standard robust optimization approaches become intractable due to the large number or non-convexity of the constraints involved in safe multi-agent control. To address this, we introduce novel robust reformulations that significantly reduce complexity without compromising safety. The applicability of the framework is further broadened to address both deterministic and stochastic uncertainties by incorporating robust chance constraints and distribution steering techniques. To achieve scalability, we derive a distributed approach based on the Alternating Direction Method of Multipliers (ADMM), supported by a convergence study that accounts for the underlying non-convexity. In addition, computational complexity bounds highlighting the efficiency of the proposed frameworks against standard approaches are presented. Finally, the robustness and scalability of the framework is demonstrated through extensive simulation results across diverse scenarios, including environments with nonconvex obstacles and up to 246 agents.
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