# Optimal Sensor and Actuator Selection using Balanced Model Reduction

## TL;DR

This paper introduces an efficient method for optimal sensor and actuator placement in high-dimensional systems using balanced model reduction and greedy QR pivoting, significantly reducing computational complexity.

## Contribution

It develops a scalable greedy algorithm for sensor and actuator selection that approximates optimal placements with linear runtime scaling.

## Key findings

- Algorithm efficiently approximates optimal placements.
- Runtime scales linearly with system dimension.
- Demonstrated on Ginzburg-Landau system, matching costly gradient descent results.

## Abstract

Optimal sensor and actuator selection is a central challenge in high-dimensional estimation and control. Nearly all subsequent control decisions are affected by these sensor/actuator locations, and optimal placement amounts to an intractable brute-force search among the combinatorial possibilities. In this work, we exploit balanced model reduction and greedy optimization to efficiently determine sensor and actuator selections that optimize observability and controllability. In particular, we determine locations that optimize scalar measures of observability and controllability via greedy matrix QR pivoting on the dominant modes of the direct and adjoint balancing transformations. Pivoting runtime scales linearly with the state dimension, making this method tractable for high-dimensional systems. The results are demonstrated on the linearized Ginzburg-Landau system, for which our algorithm approximates known optimal placements computed using costly gradient descent methods.