# Infinite-Dimensional Sums-of-Squares for Optimal Control

arXiv: https://arxiv.org/abs/2110.07396 · HTML: https://mlsanity.com/paper/2110.07396/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2021.

## Built on by (most cited first, 6 of 6)

- [Information Theory with Kernel Methods](https://mlsanity.com/paper/2202.08545/) (2022)
- [Learning PSD-valued functions using kernel sums-of-squares](https://mlsanity.com/paper/2111.11306/) (2021)
- [Non-Convex Optimization with Certificates and Fast Rates Through Kernel Sums of Squares](https://mlsanity.com/paper/2204.04970/) (2022)
- [Approximation of optimization problems with constraints through kernel Sum-Of-Squares](https://mlsanity.com/paper/2301.06339/) (2023)
- [Efficient Sampling of Stochastic Differential Equations with Positive Semi-Definite Models](https://mlsanity.com/paper/2303.17109/) (2023)
- [GloptiNets: Scalable Non-Convex Optimization with Certificates](https://mlsanity.com/paper/2306.14932/) (2023)

## Abstract (arXiv)

We introduce an approximation method to solve an optimal control problem via the Lagrange dual of its weak formulation. It is based on a sum-of-squares representation of the Hamiltonian, and extends a previous method from polynomial optimization to the generic case of smooth problems. Such a representation is infinite-dimensional and relies on a particular space of functions-a reproducing kernel Hilbert space-chosen to fit the structure of the control problem. After subsampling, it leads to a practical method that amounts to solving a semi-definite program. We illustrate our approach by a numerical application on a simple low-dimensional control problem.