Event-Triggered Gain Scheduling of 2 x 2 Linear Hyperbolic PDEs via Neural Operators (Full Version)
For control engineers dealing with real-time control of time-varying hyperbolic PDE systems, this work provides a computationally efficient method that maintains stability.
This paper introduces an event-triggered gain scheduling framework for 2x2 linear hyperbolic PDEs with time- and space-varying coefficients, using neural operators to learn the mapping from system parameters to backstepping kernels, eliminating the need to solve kernel equations at each triggering instant and reducing computational overhead while ensuring closed-loop stability.
This paper introduces a new framework for event-triggered gain scheduling applied to linear hyperbolic Partial Differential Equations (PDEs) with time- and space-varying coefficients. The approach leverages neural operators to address the challenges of real-time control in such systems. At each triggering time, the control input is designed using the classical static backstepping control law, while the gains of the boundary controller are updated according to the triggering mechanism and the spatial variation of the coefficients. Neural operators are employed to learn the mapping between the system parameters in the PDEs and the corresponding backstepping kernels. By integrating neural operators into the event-triggered framework, we eliminate the need to repeatedly solve complex kernel equations at every triggering instant, thereby reducing computational overhead while ensuring closed-loop stability. The proposed method is validated through theoretical analysis and numerical simulations, demonstrating its effectiveness and strong potential for real-time control of time-varying hyperbolic PDE systems.