# On the Optimal Control of Relaxation Systems

arXiv: https://arxiv.org/abs/1909.07219 · HTML: https://mlsanity.com/paper/1909.07219/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2019.

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

- [Mapping back and forth between model predictive control and neural networks](https://mlsanity.com/paper/2404.12030/) (2024)

## Abstract (arXiv)

The relaxation systems are an important subclass of the passive systems that arise naturally in applications. We exploit the fact that they have highly structured state-space realisations to derive analytical solutions to some simple H-infinity type optimal control problems. The resulting controllers are also relaxation systems, and often sparse. This makes them ideal candidates for applications in large-scale problems, which we demonstrate by designing simple, sparse, electrical circuits to optimally control large inductive networks and to solve linear regression problems.