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A Dynamical Approach to Efficient Eigenvalue Estimation in General Multiagent Networks

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Document pages: 12 pages

Abstract: We propose a method to efficiently estimate the eigenvalues of any arbitrary(potentially weighted and or directed) network of interacting dynamical agentsfrom dynamical observations. These observations are discrete, temporalmeasurements about the evolution of the outputs of a subset of agents(potentially one) during a finite time horizon; notably, we do not requireknowledge of which agents are contributing to our measurements. We propose anefficient algorithm to exactly recover the (potentially complex) eigenvaluescorresponding to network modes that are observable from the outputmeasurements. The length of the sequence of measurements required by our methodto generate a full reconstruction of the observable eigenvalue spectrum is, atmost, twice the number of agents in the network, but smaller in practice. Theproposed technique can be applied to networks of multiagent systems witharbitrary dynamics in both continuous- and discrete-time. Finally, weillustrate our results with numerical simulations.

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