用最优传输设计分布式多智能体分布匹配，无需全局信息
Optimal Transport-Based Decentralized Multi-Agent Distribution Matching
- 基于沃尔什斯坦距离构建本地决策机制，每智能体仅用局部信息确定目标位置
- 通过序列权重更新与记忆修正，实现通信中断下稳定收敛的分布匹配
- 适用于大规模分布式系统，尤其适合通信受限的机器人编队场景
本文提出一种用于多智能体系统（MAS）分布匹配的去中心化控制框架，使各智能体协同达成预设的终端空间分布。问题基于最优传输理论（沃尔什斯坦距离）建模，提供分布差异的合理度量，并作为控制设计基础。为避免直接求解全局最优传输问题，将分布匹配目标转化为可计算的本地决策过程，使每个智能体仅凭局部信息即可确定其期望终端位置。引入序列权重更新规则以构建可行的本地传输方案，并结合记忆增强校正机制，在间歇性、范围受限通信条件下维持可靠运行。理论证明在线性与非线性动态系统下，代理成本呈现周期性改进。仿真结果表明，该框架可在完全去中心化模式下实现高效且可扩展的分布匹配。
原文摘要 · Abstract (English)
This paper presents a decentralized control framework for distribution matching in multi-agent systems (MAS), where agents collectively achieve a prescribed terminal spatial distribution. The problem is formulated using optimal transport (Wasserstein distance), which provides a principled measure of distributional discrepancy and serves as the basis for the control design. To avoid solving the global optimal transport problem directly, the distribution-matching objective is reformulated into a tractable per-agent decision process, enabling each agent to identify its desired terminal locations using only locally available information. A sequential weight-update rule is introduced to construct feasible local transport plans, and a memory-based correction mechanism is incorporated to maintain reliable operation under intermittent and range-limited communication. Convergence guarantees are established, showing cycle-wise improvement of a surrogate transport cost under both linear and nonlinear agent dynamics. Simulation results demonstrate that the proposed framework achieves effective and scalable distribution matching while operating fully in a decentralized manner.
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