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.

翻译：本文提出了一种用于多智能体系统分布匹配的去中心化控制框架，其中智能体共同实现指定的终端空间分布。该问题采用最优传输（Wasserstein距离）进行建模，该度量提供了分布差异的原则性衡量，并作为控制设计的基础。为避免直接求解全局最优传输问题，分布匹配目标被重构为可处理的单智能体决策过程，使每个智能体仅利用局部可用信息即可确定其期望的终端位置。本文引入了一种顺序权重更新规则以构建可行的局部传输方案，并融合了一种基于记忆的校正机制，以确保在间歇性、距离受限的通信条件下维持可靠运行。理论分析建立了收敛性保证，表明在线性和非线性智能体动力学下，替代传输成本均能实现逐周期改进。仿真结果表明，所提框架在完全去中心化运行的同时，实现了高效且可扩展的分布匹配。