# Funnel control for boundary control systems

## TL;DR

This paper develops a nonlinear funnel control method for boundary control systems, ensuring prescribed performance in tracking reference signals, with proofs of solution existence and uniqueness, applicable to hyperbolic and parabolic PDEs.

## Contribution

It introduces a novel nonlinear funnel control approach for boundary control systems, providing rigorous theoretical guarantees and broad applicability.

## Key findings

- Proved existence and uniqueness of solutions for the closed-loop system.
- Demonstrated the method's applicability to hyperbolic and parabolic equations.
- Ensured prescribed performance in reference signal tracking.

## Abstract

We study a nonlinear, non-autonomous feedback controller applied to boundary control systems. Our aim is to track a given reference signal with prescribed performance. Existence and uniqueness of solutions to the resulting closed-loop system is proved by using nonlinear operator theory. We apply our results to both hyperbolic and parabolic equations.