Topology inference is a crucial problem for cooperative control in multi-agent systems. Different from most prior works, this paper is dedicated to inferring the directed network topology from the observations that consist of a single, noisy and finite time-series system trajectory, where the cooperation dynamics is stimulated with the initial network state and the unmeasurable latent input. The unmeasurable latent input refers to intrinsic system signal and extrinsic environment interference. Considering the time-invariant/varying nature of the input, we propose two-layer optimization-based and iterative estimation based topology inference algorithms (TO-TIA and IE-TIA), respectively. TO-TIA allows us to capture the separability of global agent state and eliminates the unknown influence of time-invariant input on system dynamics. IE-TIA further exploits the identifiability and estimability of more general time-varying input and provides an asymptotic solution with desired convergence properties, with higher computation cost compared with TO-TIA. Our novel algorithms relax the dependence of observation scale and leverage the empirical risk reformulation to improve the inference accuracy in terms of the topology structure and edge weight. Comprehensive theoretical analysis and simulations for various topologies are provided to illustrate the inference feasibility and the performance of the proposed algorithms.

中文翻译：

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不可测量潜在输入下多智能体合作的拓扑推理

拓扑推理是多智能体系统中协同控制的关键问题。与大多数先前的工作不同，本文致力于从由单个、嘈杂和有限时间序列系统轨迹组成的观察中推断有向网络拓扑，其中协作动态受到初始网络状态和不可测量的潜在输入的刺激. 不可测量的潜在输入是指内在系统信号和外在环境干扰。考虑到输入的时不变/变化性质，我们分别提出了基于两层优化和基于迭代估计的拓扑推理算法（TO-TIA 和 IE-TIA）。TO-TIA 允许我们捕获全局代理状态的可分离性，并消除时不变输入对系统动力学的未知影响。IE-TIA 进一步利用更一般的时变输入的可识别性和可估计性，并提供具有所需收敛特性的渐近解，与 TO-TIA 相比具有更高的计算成本。我们的新算法放宽了对观测尺度的依赖性，并利用经验风险重构来提高拓扑结构和边缘权重方面的推理精度。提供了各种拓扑的综合理论分析和仿真，以说明所提出算法的推理可行性和性能。我们的新算法放宽了对观测尺度的依赖性，并利用经验风险重构来提高拓扑结构和边缘权重方面的推理精度。提供了各种拓扑的综合理论分析和仿真，以说明所提出算法的推理可行性和性能。我们的新算法放宽了对观测尺度的依赖性，并利用经验风险重构来提高拓扑结构和边缘权重方面的推理精度。提供了各种拓扑的综合理论分析和仿真，以说明所提出算法的推理可行性和性能。