提出一种可证明收敛的分布式多智能体覆盖方法，提升资源受限任务中的覆盖率与稳定性。
Density-Driven Optimal Control: Convergence Guarantees for Stochastic LTI Multi-Agent Systems
- 基于随机LTI系统建模，用Wasserstein距离优化分布匹配
- 理论保证在噪声下时间平均分布收敛到目标密度，误差有界
- 无需复杂求解器，适合高优先级空间覆盖场景
本文针对具有高空间优先级和资源约束的任务，解决多智能体系统的去中心化非均匀区域覆盖问题。现有基于密度的方法常依赖计算量大的欧拉型偏微分方程求解器或启发式规划，本文提出随机密度驱动最优控制（Stochastic D²OC），这是一种严格的拉格朗日框架，将个体智能体动态与集体分布匹配相衔接。通过构建类似模型预测控制的随机优化问题，以Wasserstein距离作为运行代价，确保在随机线性时不变（LTI）动态下，时间平均经验分布收敛至非参数目标密度。关键贡献在于通过可达性分析建立了形式化收敛性保证，在过程与测量噪声存在时仍能保持有界跟踪误差。数值结果表明，随机D²OC实现了鲁棒、去中心化的覆盖效果，且在最优性与一致性上优于以往启发式方法。
原文摘要 · Abstract (English)
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 (D$^2$OC). 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 D$^2$OC achieves robust, decentralized coverage while outperforming previous heuristic methods in optimality and consistency.
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