# An adaptive POD approximation method for the control of advection-diffusion equations

arXiv: https://arxiv.org/abs/1302.4072 · HTML: https://mlsanity.com/paper/1302.4072/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2013.

## Built on by (most cited first, 1 of 1)

- [A Reduced Order Iterative Linear Quadratic Regulator (ILQR) Technique for the Optimal Control of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/2501.06635/) (2025)

## Abstract (arXiv)

We present an algorithm for the approximation of a finite horizon optimal control problem for advection-diffusion equations. The method is based on the coupling between an adaptive POD representation of the solution and a Dynamic Programming approximation scheme for the corresponding evolutive Hamilton-Jacobi equation. We discuss several features regarding the adaptivity of the method, the role of error estimate indicators to choose a time subdivision of the problem and the computation of the basis functions. Some test problems are presented to illustrate the method.