# Polyhedral Control Design: Theory and Methods

arXiv: https://arxiv.org/abs/2412.13082 · HTML: https://mlsanity.com/paper/2412.13082/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2024.

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

- [ShardNet: Training Neural Controllers with Hard, Non-Convex Constraints](https://mlsanity.com/paper/2606.30935/) (2026)

## Abstract (arXiv)

In this article, we survey the primary research on polyhedral computing methods for constrained linear control systems. Our focus is on the modeling power of convex optimization, featured to design set-based robust and optimal controllers. In detail, we review the state-of-the-art techniques for computing geometric structures such as robust control invariant polytopes. Moreover, we survey recent methods for constructing control Lyapunov functions with polyhedral epigraphs as well as the extensive literature on robust model predictive control. The article concludes with a discussion of both the complexity and potential of polyhedral computing methods that rely on large-scale convex optimization.