Delay-Adaptive Control of First-order Hyperbolic PIDEs
Analysis of PDEs
2023-07-11 v1 Systems and Control
Systems and Control
Optimization and Control
Classical Physics
Fluid Dynamics
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
Cite
@article{arxiv.2307.04212,
title = {Delay-Adaptive Control of First-order Hyperbolic PIDEs},
author = {Shanshan Wang and Jie Qi and Miroslav Krstic},
journal= {arXiv preprint arXiv:2307.04212},
year = {2023}
}