Austin Copeland | Searcharxiv

arXiv2026

A Temporal Cellular Sheaf Framework for Multi-Agent Systems with Switching Communication Topologies

Cellular sheaves serve as a natural modeling framework for encoding heterogeneity in the state and interaction spaces of multi-agent systems. This work examines switching communication graphs with the use of temporal cellular sheaves, which we construct to represent heterogeneous agent state spaces, the maps that relate them, and their respective communication constraints. We then develop sufficient conditions under which a multi-agent system defined on a temporal cellular sheaf can solve the target tracking problem by generalizing the existing concept of joint connectivity. Using a Lyapunov-based stability analysis, we demonstrate that the target tracking error of the network converges to a neighborhood of the origin.

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arXiv2025

Heterogeneous Multi-Agent Multi-Target Tracking using Cellular Sheaves

Multi-agent target tracking in the presence of nonlinear dynamics and agent heterogeneity, where state-space dimensions may differ, is a challenging problem that traditional graph Laplacian methods cannot easily address. This work leverages the framework of cellular sheaves, a mathematical generalization of graph theory, to natively model such heterogeneous systems. While existing coordination sheaf frameworks focus on cooperative problems like consensus, this work extends them to the non-cooperative target-tracking problem. The tracking of multiple, unknown targets is formulated as a harmonic extension problem on a cellular sheaf, accommodating nonlinear dynamics and external disturbances for all agents. A decentralized control law is developed using the sheaf Laplacian, and a corresponding Lyapunov-based stability analysis is provided to guarantee tracking error convergence, with results validated by simulation.

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