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Decentralized Continuification Control of Multi-Agent Systems via Distributed Density Estimation

Beniamino Di Lorenzo, Gian Carlo Maffettone, Mario di Bernardo

TL;DR

The paper tackles decentralized density control for large swarms on a circle by marrying continuification with distributed density estimation. It replaces centralized macroscopic observables with a KDE-based density estimate fused through PI consensus, allowing each agent to compute local controls $u_i$ from its own density estimate. The approach yields macroscopic convergence comparable to centralized methods across regulation and tracking tasks, even under time-varying topologies, while highlighting robustness to communication constraints. This work advances scalable, reliable multi-agent density control in distributed networks and outlines paths for extending the method to higher dimensions and more complex communication scenarios.

Abstract

This paper introduces a novel decentralized implementation of a continuification-based strategy to control the density of large-scale multi-agent systems on the unit circle. While continuification methods effectively address micro-to-macro control problems by reformulating ordinary/stochastic differential equations (ODEs/SDEs) agent-based models into more tractable partial differential equations (PDEs), they traditionally require centralized knowledge of macroscopic state observables. We overcome this limitation by developing a distributed density estimation framework that combines kernel density estimation with PI consensus dynamics. Our approach enables agents to compute local density estimates and derive local control actions using only information from neighboring agents in a communication network. Numerical validations across multiple scenarios - including regulation, tracking, and time-varying communication topologies - confirm the effectiveness of the proposed approach. They also convincingly demonstrate that our decentralized implementation achieves performance comparable to centralized approaches while enhancing reliability and practical applicability.

Decentralized Continuification Control of Multi-Agent Systems via Distributed Density Estimation

TL;DR

The paper tackles decentralized density control for large swarms on a circle by marrying continuification with distributed density estimation. It replaces centralized macroscopic observables with a KDE-based density estimate fused through PI consensus, allowing each agent to compute local controls from its own density estimate. The approach yields macroscopic convergence comparable to centralized methods across regulation and tracking tasks, even under time-varying topologies, while highlighting robustness to communication constraints. This work advances scalable, reliable multi-agent density control in distributed networks and outlines paths for extending the method to higher dimensions and more complex communication scenarios.

Abstract

This paper introduces a novel decentralized implementation of a continuification-based strategy to control the density of large-scale multi-agent systems on the unit circle. While continuification methods effectively address micro-to-macro control problems by reformulating ordinary/stochastic differential equations (ODEs/SDEs) agent-based models into more tractable partial differential equations (PDEs), they traditionally require centralized knowledge of macroscopic state observables. We overcome this limitation by developing a distributed density estimation framework that combines kernel density estimation with PI consensus dynamics. Our approach enables agents to compute local density estimates and derive local control actions using only information from neighboring agents in a communication network. Numerical validations across multiple scenarios - including regulation, tracking, and time-varying communication topologies - confirm the effectiveness of the proposed approach. They also convincingly demonstrate that our decentralized implementation achieves performance comparable to centralized approaches while enhancing reliability and practical applicability.

Paper Structure

This paper contains 14 sections, 1 theorem, 24 equations, 9 figures.

Table of Contents

  1. INTRODUCTION
  2. Model and Problem Statement
  3. CENTRALIZED CONTROL DESIGN
  4. Continuification
  5. Macroscopic control design
  6. Discretization
  7. Decentralized continuification control
  8. Distributed density estimation
  9. APPLICATION TO MULTI-AGENT SYSTEMS
  10. Regulation
  11. Tracking
  12. Proximity communication network
  13. Increasing number of neighbors
  14. CONCLUSIONS

Key Result

Theorem 1

Choosing where $K_\mathrm{p}$ is a positive control gain, the error dynamics globally asymptotically pointwisely converges to 0.

Figures (9)

  • Figure 1: Continuification control pipeline, inspired by nikitin2021continuation.
  • Figure 2: Schematization of agents interactions and communication. Agents physically influence each other through the interaction topology, and exchange information via the communication layer.
  • Figure 3: (a) Block diagram: individual agents compute their own macroscopic control action $U^{(i)}$ depending on their local estimate of the density. (b) Detail of the distributed density estimator.
  • Figure 4: Bimodal regulation trial. (a) Initial (inner circle) and final configuration (outer circle) of agents controlled with the centralized strategy, (b) initial (solid blue), final (solid orange) and desired (dashed black) densities; (c) initial (inner circle) and final (outer circle) configuration of agents controlled with the decentralized strategy, (d) initial (solid blue), final (solid orange) and desired (dashed black) densities.
  • Figure 5: Bimodal regulation trial. (a) Comparison between density errors obtained with centralized and decentralized strategies; (b) estimation error with inset restricting the time interval to [0,1].
  • ...and 4 more figures

Theorems & Definitions (2)

  • Theorem 1: Macroscopic Convergence
  • proof