Nussbaum-Based Adaptive Neural Network Event-Triggered Control for Hyperbolic PDE Systems With Uncertain Actuator Dynamics and Deception Attacks

This paper explores the security control problem of a class of hyperbolic partial differential equation (PDE) systems described by a set of nonlinear ordinary differential equation (ODE) under deception attacks. Compared with the control design process of traditional single ODE systems, the strong coupling characteristics of partial differential equation-ordinary differential equation (PDE-ODE) systems make the control design under deception attacks more difficult. By applying the infinite-dimensional backstepping transformation and its inverse transformation, the original PDE subsystem is transformed into a more tractable target system, thus effectively achieving control performance. The neural network approximation algorithm is adopted to separate the coupling effects caused by attacks, focusing on addressing the unknown nonlinear dynamics of the system. Deception attacks are modeled as time-varying weights with unknown control directions, and the Nussbaum function is employed to address the problem of unknown control directions. In addition, a dynamic event-triggered mechanism with a novel switching threshold is designed to alleviate the communication burden. The proposed control algorithm ensures that both the closed-loop system states and the actuator states are bounded. Finally, this conclusion is verified through numerical simulation.