2024/11/30 by Yuhang Mei, Mohammad Al-Jarrah, Mei, Yuhang +5 · 3 citations
Computer Science · Decision Sciences · Engineering · #Advanced Control Systems Optimization #FOS: Mathematics #Optimization and Control (math.OC) #Reinforcement Learning in Robotics #Simulation Techniques and Applications
paper · pdf · doi:10.48550/arxiv.2412.00617
openalex publication_date 2024/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper addresses the problem of steering an initial probability distribution to a target probability distribution through a deterministic or stochastic linear control system. Our proposed approach is inspired by the flow matching methodology, with the difference that we can only affect the flow through the given control channels. The motivation comes from applications such as robotic swarms and stochastic thermodynamics, where agents or particles can only be manipulated through control actions. The feedback control law that achieves the task is characterized as the conditional expectation of the control inputs for the stochastic bridges that respect the given control system dynamics. Explicit forms are derived for special cases, and a numerical procedure is presented to approximate the control law, illustrated with examples.