Density-Driven Optimal Control: Convergence Guarantees for Stochastic LTI Multi-Agent Systems

• URL: http://arxiv.org/abs/2604.08495v1
• Date: Thu, 09 Apr 2026 17:39:25 GMT
• Title: Density-Driven Optimal Control: Convergence Guarantees for Stochastic LTI Multi-Agent Systems
• Abstract summary: This paper addresses the decentralized non-uniform area coverage problem for multi-agent systems.<n>We propose Density-Driven Optimal Control (D$2$OC)<n>This is a rigorous Lagrangian framework that bridges the gap between individual agent dynamics and collective distribution matching.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 (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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