# Output-Feedback Boundary Control of a Heat PDE Sandwiched Between Two ODEs

arXiv: https://arxiv.org/abs/1902.04480 · HTML: https://mlsanity.com/paper/1902.04480/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2019.

## Built on by (most cited first, 2 of 2)

- [Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEs](https://mlsanity.com/paper/2303.10506/) (2023)
- [Machine Learning Accelerated PDE Backstepping Observers](https://mlsanity.com/paper/2211.15044/) (2022)

## Abstract (arXiv)

We present designs for exponential stabilization of an ODE-heat PDE-ODE coupled system where the control actuation only acts in one ODE. The combination of PDE backstepping and ODE backstepping is employed in a state-feedback control law and in an observer that estimates PDE and two ODE states only using one PDE boundary measurement. Based on the state-feedback control law and the observer, the output-feedback control law is then proposed. The exponential stability of the closed-loop system and the boundedness and exponential convergence of the control law are proved via Lyapunov analysis. Finally, numerical simulations validate the effectiveness of this method for the `sandwiched' system.