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.

翻译：在非线性动力学和智能体异构性（状态空间维度可能不同）存在的条件下，多智能体目标跟踪是一个传统图拉普拉斯方法难以解决的挑战性问题。本研究利用胞腔层（图论的数学推广）框架，原生地对此类异构系统进行建模。现有的协调层框架主要关注如共识等合作性问题，而本工作将其扩展至非合作的目标跟踪问题。多个未知目标的跟踪被表述为胞腔层上的调和延拓问题，能够适应所有智能体的非线性动力学和外部干扰。利用层拉普拉斯算子，我们提出了一种分散式控制律，并提供了相应的基于李雅普诺夫方法的稳定性分析，以保证跟踪误差的收敛性，仿真结果验证了该方法的有效性。