Density-Driven Optimal Control: Convergence Guarantees for Stochastic LTI Multi-Agent Systems
Abstract
This paper addresses the decentralized non-uniform area coverage problem for multi-agent systems, a critical task in missions with high spatial priority and resource constraints. While existing density-based methods often rely on computationally heavy Eulerian PDE solvers or heuristic planning, we propose Stochastic Density-Driven Optimal Control (DOC). This is a rigorous Lagrangian framework that bridges the gap between individual agent dynamics and collective distribution matching. By formulating a stochastic MPC-like problem that minimizes the Wasserstein distance as a running cost, our approach ensures that the time-averaged empirical distribution converges to a non-parametric target density under stochastic LTI dynamics. A key contribution is the formal convergence guarantee established via reachability analysis, providing a bounded tracking error even in the presence of process and measurement noise. Numerical results verify that Stochastic DOC achieves robust, decentralized coverage while outperforming previous heuristic methods in optimality and consistency.
Cite
@article{arxiv.2604.08495,
title = {Density-Driven Optimal Control: Convergence Guarantees for Stochastic LTI Multi-Agent Systems},
author = {Kooktae Lee},
journal= {arXiv preprint arXiv:2604.08495},
year = {2026}
}