# Small-time global approximate controllability of bilinear wave equations

arXiv: https://arxiv.org/abs/2305.11794 · HTML: https://mlsanity.com/paper/2305.11794/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2023.

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

- [Control and optimization for Neural Partial Differential Equations in Supervised Learning](https://mlsanity.com/paper/2506.20764/) (2025)

## Abstract (arXiv)

We consider a bilinear control problem for the wave equation on a torus of arbitrary dimension. We show that the system is globally approximately controllable in arbitrarily small times from a dense family of initial states. The control strategy is explicit, and based on a small-time limit of conjugated dynamics to move along non-directly accessible directions (a.k.a. Lie brackets of the generators).