A Dynamical Approach to Efficient Eigenvalue Estimation in General Multiagent Networks

07/09/2020

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by   Mikhail Hayhoe, et al.

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We propose a method to efficiently estimate the eigenvalues of any arbitrary, unknown network of interacting dynamical agents. The inputs to our estimation algorithm are 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 eigenvalues corresponding directly to those modes that are recoverable from our measurements. We show how our 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.