A Passivity-Based Network Identification Algorithm with Minimal Time Complexity

The theory of network identification, namely identifying the (weighted) interaction topology among a known number of agents, has been widely developed for linear agents over recent years. However, the theory for nonlinear agents is far less developed, and non-applicable to large systems due to long running times. We use the notion of maximal equilibrium-independent passivity (MEIP) and network optimization theory to present a network identification method for nonlinear agents. We do so by first designing a sub-cubic time algorithm for LTI agents, and then augment it by linearization to achieve a sub-cubic time algorithm for network reconstruction for nonlinear agents and controllers. Lastly, we study the problem of network reconstruction from a complexity theory standpoint, showing that the presented algorithms are in fact optimal in terms of time complexity. We provide examples of reconstructing large-scale networks, including a network of first-order linear agents, and a non-linear neural network model.

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