# Feedback control of parametrized PDEs via model order reduction and dynamic programming principle

arXiv: https://arxiv.org/abs/1810.00021 · HTML: https://mlsanity.com/paper/1810.00021/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2018.

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

- [Real-time optimal control of high-dimensional parametrized systems by deep learning-based reduced order models](https://mlsanity.com/paper/2409.05709/) (2024)
- [Latent feedback control of distributed systems in multiple scenarios through deep learning-based reduced order models](https://mlsanity.com/paper/2412.09942/) (2024)
- [Real-time optimal control with shallow recurrent decoder networks](https://mlsanity.com/paper/2607.19302/) (2026)

## Abstract (arXiv)

In this paper we investigate infinite horizon optimal control problems for parametrized partial differential equations. We are interested in feedback control via dynamic programming equations which is well-known to suffer from the curse of dimensionality. Thus, we apply parametric model order reduction techniques to construct low-dimensional subspaces with suitable information on the control problem, where the dynamic programming equations can be approximated. To guarantee a low number of basis functions, we combine recent basis generation methods and parameter partitioning techniques. Furthermore, we present a novel technique to construct nonuniform grids in the reduced domain, which is based on statistical information. Finally, we discuss numerical examples to illustrate the effectiveness of the proposed methods for PDEs in two space dimensions.