# Approximate abstractions of control systems with an application to aggregation

arXiv: https://arxiv.org/abs/1809.03621 · HTML: https://mlsanity.com/paper/1809.03621/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2018.

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

- [Transfer Learning for Control Systems via Neural Simulation Relations](https://mlsanity.com/paper/2412.01783/) (2024)

## Abstract (arXiv)

Previous approaches to constructing abstractions for control systems rely on geometric conditions or, in the case of an interconnected control system, a condition on the interconnection topology. Since these conditions are not always satisfiable, we relax the restrictions on the choice of abstractions, instead opting to select ones which nearly satisfy such conditions via optimization-based approaches. To quantify the resulting effect on the error between the abstraction and concrete control system, we introduce the notions of practical simulation functions and practical storage functions. We show that our approach facilitates the procedure of aggregation, where one creates an abstraction by partitioning agents into aggregate areas. We demonstrate the results on an application where we regulate the temperature in three separate zones of a building.