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In this paper, we propose a novelty-based metric for quantitativecharacterization of the controllability of complex networks. This inherentlybounded metric describes the average angular separation of an input withrespect to the past input history. We use this metric to find the minimallynovel input that drives a linear network to a desired state using unit averageenergy. Specifically, the minimally novel input is defined as the solution of acontinuous time, non-convex optimal control problem based on the introducedmetric. We provide conditions for existence and uniqueness, and an explicit,closed-form expression for the solution. We support our theoretical results bycharacterizing the minimally novel inputs for an example of a recurrentneuronal network.

Controlling Linear Networks with Minimally Novel Inputs