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

2026-04-09

AI Summary

This work addresses the decentralized non-uniform coverage problem for multi-agent systems under resource constraints and high spatial priority tasks by proposing a Stochastic Density-Driven Optimal Control (D²OC) approach. The method formulates a Lagrangian framework under stochastic linear time-invariant (LTI) dynamics, minimizing the Wasserstein distance as the running cost to drive the empirical distribution of agents toward a nonparametric target density. It provides the first formal convergence guarantee for stochastic LTI multi-agent systems and integrates reachability analysis to ensure bounded tracking errors in the presence of process and measurement noise. Numerical experiments demonstrate that the proposed method significantly outperforms existing heuristic strategies in both coverage optimality and consensus, achieving robust decentralized coverage.

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.

Problem

• decentralized coverage
• non-uniform area coverage
• multi-agent systems
• stochastic LTI systems
• density-driven control

Innovation

• Stochastic Density-Driven Optimal Control
• Wasserstein distance
• decentralized coverage
• convergence guarantee
• stochastic LTI systems