# The turnpike property in semilinear control

arXiv: https://arxiv.org/abs/2004.03269 · HTML: https://mlsanity.com/paper/2004.03269/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2020.

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

- [Turnpike in optimal control of PDEs, ResNets, and beyond](https://mlsanity.com/paper/2202.04097/) (2022)

## Abstract (arXiv)

An exponential turnpike property for a semilinear control problem is proved. The state-target is assumed to be small, whereas the initial datum can be arbitrary. Turnpike results are also obtained for large targets, requiring that the control acts everywhere. In this case, we prove the convergence of the infimum of the averaged time-evolution functional towards the steady one. Numerical simulations are performed.