Controlling Linear Networks with Minimally Novel Inputs

TL;DR

This paper introduces a new metric for network controllability based on input novelty, and derives a closed-form solution for minimally novel inputs that steer linear networks to desired states with minimal deviation from past inputs.

Contribution

It proposes a novel bounded metric for network controllability and provides explicit solutions for minimally novel inputs in linear networks.

Findings

Derived conditions for existence and uniqueness of solutions.

Provided a closed-form expression for minimally novel inputs.

Validated results with a recurrent neuronal network example.

Abstract

In this paper, we propose a novelty-based metric for quantitative characterization of the controllability of complex networks. This inherently bounded metric describes the average angular separation of an input with respect to the past input history. We use this metric 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 metric. 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.