# Error analysis for POD Approximations of infinite horizon problems via the Dynamic Programming approach

arXiv: https://arxiv.org/abs/1511.00265 · HTML: https://mlsanity.com/paper/1511.00265/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2015.

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

- [SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problems](https://mlsanity.com/paper/2201.05475/) (2022)
- [Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs](https://mlsanity.com/paper/2105.03336/) (2021)
- [Optimal Control of Agent-Based Dynamics under Deep Galerkin Feedback Laws](https://mlsanity.com/paper/2406.09141/) (2024)

## Abstract (arXiv)

In this paper infinite horizon optimal control problems for nonlinear high-dimensional dynamical systems are studied. Nonlinear feedback laws can be computed via the value function characterized as the unique viscosity solution to the corresponding Hamilton-Jacobi-Bellman (HJB) equation which stems from the dynamic programming approach. However, the bottleneck is mainly due to the curse of dimensionality and HJB equations are only solvable in a relatively small dimension. Therefore, a reduced-order model is derived for the dynamical system and for this purpose the method of proper orthogonal decomposition (POD) is used. The resulting errors in the HJB equations are estimated by an a-priori error analysis, which suggests a new sampling strategy for the POD method. Numerical experiments illustrates the theoretical findings.