# Delay-Adaptive Control of First-order Hyperbolic PIDEs

arXiv: https://arxiv.org/abs/2307.04212 · HTML: https://mlsanity.com/paper/2307.04212/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2023.

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

- [Deep Learning of Delay-Compensated Backstepping for Reaction-Diffusion PDEs](https://mlsanity.com/paper/2308.10501/) (2023)

## Abstract (arXiv)

We develop a delay-adaptive controller for a class of first-order hyperbolic partial integro-differential equations (PIDEs) with an unknown input delay. By employing a transport PDE to represent delayed actuator states, the system is transformed into a transport partial differential equation (PDE) with unknown propagation speed cascaded with a PIDE. A parameter update law is designed using a Lyapunov argument and the infinite-dimensional backstepping technique to establish global stability results. Furthermore, the well-posedness of the closed-loop system is analyzed. Finally, the effectiveness of the proposed method was validated through numerical simulations