Delay-Adaptive Control of First-order Hyperbolic PIDEs

TL;DR

This paper introduces a delay-adaptive control method for first-order hyperbolic PIDEs with unknown delays, transforming the system into a cascade of PDEs and PIDEs, and validating stability and effectiveness through simulations.

Contribution

It presents a novel delay-adaptive control approach using backstepping for hyperbolic PIDEs with unknown delays, including stability analysis and numerical validation.

Findings

Global stability of the closed-loop system is established.

The control method effectively compensates for unknown input delays.

Numerical simulations confirm the theoretical results.

Abstract

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