# Optimal Sensor and Actuator Selection using Balanced Model Reduction

arXiv: https://arxiv.org/abs/1812.01574 · HTML: https://mlsanity.com/paper/1812.01574/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2018.

## Built on by (most cited first, 3 of 3)

- [Constrained optimization of sensor placement for nuclear digital twins](https://mlsanity.com/paper/2306.13637/) (2023)
- [Data-Induced Interactions of Sparse Sensors Using Statistical Physics](https://mlsanity.com/paper/2307.11838/) (2023)
- [Generalized Inverses of Matrix Products: From Fundamental Subspaces to Randomized Decompositions](https://mlsanity.com/paper/2602.00386/) (2026)

## Abstract (arXiv)

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.