Density-Driven Optimal Control: Convergence Guarantees for Stochastic LTI Multi-Agent Systems
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910117145870336 |
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| author | Lee, Kooktae |
| author_facet | Lee, Kooktae |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08495 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Density-Driven Optimal Control: Convergence Guarantees for Stochastic LTI Multi-Agent Systems Lee, Kooktae Optimization and Control Multiagent Systems Robotics Systems and Control 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. |
| title | Density-Driven Optimal Control: Convergence Guarantees for Stochastic LTI Multi-Agent Systems |
| topic | Optimization and Control Multiagent Systems Robotics Systems and Control |
| url | https://arxiv.org/abs/2604.08495 |