# HJB-POD feedback control for Navier-Stokes equations

arXiv: https://arxiv.org/abs/1405.1209 · HTML: https://mlsanity.com/paper/1405.1209/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 May 2014.

## 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 report we present the approximation of an infinite horizon optimal control problem for the evolutive Navier-Stokes system. The method is based on a model reduction technique, using a POD approximation, coupled with a Hamilton-Jacobi equation which characterizes the value function of the corresponding control problem for the reduced system. Although the approximation schemes available for the HJB are shown to be convergent for any dimension, in practice we need to restrict the dimension to rather small numbers and this limitation affects the accuracy of the POD approximation. We will present numerical tests for the control of the time-dependent Navier-Stokes system in two-dimensional spatial domains to illustrate our approach and to show the effectiveness of the method.