Controlling linear networks with minimally novel inputs

In this paper, we propose a novelty-based index for quantitative characterization of the controllability of complex networks. This inherently bounded index describes the average angular separation of an input with respect to the past input history. We use this index to find the minimally novel input that drives a linear network to a desired state using unit average energy. Specifically, the minimally novel input is defined as the solution of a continuous time, non-convex optimal control problem based on the introduced index. We provide conditions for existence and uniqueness, and an explicit, closed-form expression for the solution. We support our theoretical results by characterizing the minimally novel inputs for an example of a recurrent neuronal network.