Delay-Adaptive Control of First-order Hyperbolic PIDEs

2023/07/09 by Shanshan Wang, Jie Qi, Wang, Shanshan +3
Computer Science · Engineering · Mathematics · #Analysis of PDEs (math.AP) #Classical Physics (physics.class-ph) #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Nonlinear Dynamics and Pattern Formation #Numerical methods for differential equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2307.04212

openalex publication_date 2023/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

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