arXiv:2611.03981 · v1

Rapid Mean-Field Formation Transport with a Shared-Representation Neural Fokker-Planck Controller

首次提交 2026-11-03 05:21

版本更新 2026-11-03 05:21

雷达观测 2026-11-04 23:40

摘要

This paper develops a mean-field formation transport method with low online computational cost for large-scale multi-agent systems. Classical mean-field planners often require repeated solutions of coupled forward and backward partial differential equations, making online replanning computationally demanding. Density and control are therefore approximated by a common parameterized nonlinear map with separate scalar density and vector control outputs. Parameters are optimized using Fokker--Planck and initial-condition residuals, formation-matching costs on numerically simulated closed-loop particle trajectories, and control effort. Numerical computations are restricted to a bounded region of the state space, with an additional penalty on probability flux across its boundary. For the periodic-domain model, we establish well-posedness of the induced density evolution and bound the density-approximation error in terms of the dynamics and initial-condition residuals. Parameter optimization precedes online operation, during which controller coefficients remain fixed. Experiments quantify the accuracy--runtime trade-off relative to a mean-field planner, show lower transport error than classical feedback baselines, and demonstrate the benefits of the common parameterization.

作者备注：Accepted for publication in the 2026 IEEE Conference on Decision and Control (CDC)