Assignment-Free Real-time Tracking Control for Large-Scale Multi-Agent Systems

Abstract

This paper studies real time formation control for large scale multi agent systems (LMAS) with anonymous agents and finite time requirements. Instead of solving a centralized Hamilton Jacobi Bellman (HJB) problem or a coupled mean field game system, we design an assignment free controller directly at the distribution level. The swarm state is represented by a time varying probability density governed by a Fokker Planck equation with diffusion. We propose a Fokker Planck Neural Network (FPNN) to learn an admissible density evolution and a shared linear feedback law that satisfy the PDE residual, initial terminal constraints, and mass conservation on bounded domains. To quantify the performance tradeoff, we derive Riccati residual based certificates that upper bound the optimality loss relative to the centralized LQR benchmark. Simulations validate that the learned density evolution is consistent with classical PDE solvers, that the induced drift generates matching agent level trajectories for large populations, and that the overall computation cost is reduced by orders of magnitude compared with iterative mean field game solvers.