论文标题
在一般多基金网络中的有效特征值估计的动力学方法
A Dynamical Approach to Efficient Eigenvalue Estimation in General Multiagent Networks
论文作者
论文摘要
我们提出了一种方法，以有效地估算从动力学观测的任何任意加权和/或有指示的）网络的特征值。这些观察结果是关于在有限的时间范围内（可能是一个）子集（可能是一个）输出的演变的离散时间测量。值得注意的是，我们不需要了解哪些代理会为我们的测量做出贡献。我们提出了一种有效的算法，以精确恢复与来自输出测量值可观察到的网络模式相对应的（潜在复杂的）特征值。我们方法所需的测量序列的长度以生成可观察到的特征值频谱的完整重建最多是网络中的代理数量的两倍，但实际上是较小的。所提出的技术可以应用于在连续和离散时间内都具有任意动态的多种系统网络。最后，我们通过数值模拟说明了结果。
We propose a method to efficiently estimate the eigenvalues of any arbitrary (potentially weighted and/or directed) network of interacting dynamical agents from dynamical observations. These observations are discrete, temporal measurements about the evolution of the outputs of a subset of agents (potentially one) during a finite time horizon; notably, we do not require knowledge of which agents are contributing to our measurements. We propose an efficient algorithm to exactly recover the (potentially complex) eigenvalues corresponding to network modes that are observable from the output measurements. The length of the sequence of measurements required by our method to generate a full reconstruction of the observable eigenvalue spectrum is, at most, twice the number of agents in the network, but smaller in practice. The proposed technique can be applied to networks of multiagent systems with arbitrary dynamics in both continuous- and discrete-time. Finally, we illustrate our results with numerical simulations.
