On (Non)Supermodularity of Average Control Energy

TL;DR

This paper investigates the properties of average control energy in linear systems, revealing that it is not necessarily supermodular, which corrects previous misconceptions in the literature.

Contribution

It demonstrates that the expected control energy function is not always supermodular, challenging prior assumptions and clarifying the mathematical behavior of control energy.

Findings

Average control energy is not necessarily supermodular.

Corrects misconceptions in existing literature.

Provides insights into control energy properties.

Abstract

Given a linear system, we consider the expected energy to move from the origin to a uniformly random point on the unit sphere as a function of the set of actuated variables. We show this function is not necessarily supermodular, correcting some claims in the existing literature.