Optimal Transport-Based Decentralized Multi-Agent Distribution Matching

TL;DR

This paper introduces a decentralized control method for multi-agent systems that uses optimal transport theory to match a desired distribution, ensuring scalability and robustness with local decision-making and communication constraints.

Contribution

It develops a novel decentralized framework leveraging optimal transport for distribution matching, with local decision rules and convergence guarantees, improving scalability and robustness.

Findings

Effective distribution matching demonstrated in simulations

Framework maintains operation under communication limitations

Convergence guarantees established for linear and nonlinear dynamics

Abstract

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.