# Submodularity of Energy Related Controllability Metrics

arXiv: https://arxiv.org/abs/1403.6351 · HTML: https://mlsanity.com/paper/1403.6351/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2014.

## Built on by (most cited first, 2 of 2)

- [Maximum diffusion reinforcement learning](https://mlsanity.com/paper/2309.15293/) (2023)
- [Controllability of Coarsely Measured Networked Linear Dynamical Systems (Extended Version)](https://mlsanity.com/paper/2206.10569/) (2022)

## Abstract (arXiv)

The quantification of controllability and observability has recently received new interest in the context of large, complex networks of dynamical systems. A fundamental but computationally difficult problem is the placement or selection of actuators and sensors that optimize real-valued controllability and observability metrics of the network. We show that several classes of energy related metrics associated with the controllability Gramian in linear dynamical systems have a strong structural property, called submodularity. This property allows for an approximation guarantee by using a simple greedy heuristic for their maximization. The results are illustrated for randomly generated systems and for placement of power electronic actuators in a model of the European power grid.