MeanFlow Meets Control: Scaling Sampled-Data Control for Swarms

2026-03-20

AI Summary

This work addresses the challenge of efficiently steering large-scale linear time-invariant swarm systems under limited control updates and intermittent sampled inputs. The authors propose a control-space learning framework that, for the first time, integrates the MeanFlow paradigm into sampled-data control. By parameterizing the coefficients of finite-horizon minimum-energy control and leveraging bridge-trajectory analysis to uncover its integral representation and associated local differential identities, the method constructs a training objective that obviates backpropagation through dynamics. The resulting strategy inherently respects physical actuation constraints, directly models minimum-energy inputs in control space, and achieves significantly improved steering efficiency while maintaining scalability and consistency with realistic sampling structures.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Behavior Learning & Control
• Machine Learning: Learning with Manifolds

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Steering large-scale swarms in only a few control updates is challenging because real systems operate in sampled-data form: control inputs are updated intermittently and applied over finite intervals. In this regime, the natural object is not an instantaneous velocity field, but a finite-window control quantity that captures the system response over each sampling interval. Inspired by MeanFlow, we introduce a control-space learning framework for swarm steering under linear time-invariant dynamics. The learned object is the coefficient that parameterizes the finite-horizon minimum-energy control over each interval. We show that this coefficient admits both an integral representation and a local differential identity along bridge trajectories, which leads to a simple stop-gradient training objective. At implementation time, the learned coefficient is used directly in sampled-data updates, so the prescribed dynamics and actuation map are respected by construction. The resulting framework provides a scalable approach to few-step swarm steering that is consistent with the sampled-data structure of real control systems.

Problem

• sampled-data control
• swarm steering
• large-scale swarms
• finite-horizon control
• control updates

Innovation

• sampled-data control
• swarm steering
• MeanFlow
• minimum-energy control
• control-space learning