# Delay-robust control design for two heterodirectional linear coupled hyperbolic PDEs

arXiv: https://arxiv.org/abs/1709.04274 · HTML: https://mlsanity.com/paper/1709.04274/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Sep 2017.

## Built on by (most cited first, 3 of 3)

- [Neural Operators for PDE Backstepping Control of First-Order Hyperbolic PIDE with Recycle and Delay](https://mlsanity.com/paper/2307.11436/) (2023)
- [Deep Learning of Delay-Compensated Backstepping for Reaction-Diffusion PDEs](https://mlsanity.com/paper/2308.10501/) (2023)
- [Proximal Policy Optimization Learning based Control of Congested Freeway Traffic](https://mlsanity.com/paper/2204.05627/) (2022)

## Abstract (arXiv)

We detail in this article the necessity of a change of paradigm for the delay-robust control of systems composed of two linear first order hyperbolic equations. One must go back to the classical trade-off between convergence rate and delay-robustness. More precisely, we prove that, for systems with strong reflections, canceling the reflection at the actuated boundary will yield zero delay-robustness. Indeed, for such systems, using a backstepping-controller, the corresponding target system should preserve a small amount of this reflection to ensure robustness to a small delay in the loop. This implies, in some cases, giving up finite time convergence.