Neural operators enable real-time control of hyperbolic PDEs

This paper presents a novel framework for event-triggered gain scheduling of 2x2 linear hyperbolic Partial Differential Equations (PDEs) with time- and space-varying coefficients. The core challenge in real-time control of such systems is the need to repeatedly solve complex kernel equations at each control update, which is computationally prohibitive. The authors leverage neural operators—a class of deep learning models that learn mappings between function spaces—to predict the backstepping kernels directly from the system parameters. At each triggering event, the controller updates its gains using these predicted kernels, eliminating the need for online kernel solving.

The framework is validated through theoretical stability analysis and numerical simulations, showing that the event-triggered approach with neural operators maintains closed-loop stability while drastically reducing computational overhead. This makes it highly suitable for real-time applications such as adaptive optics, fluid flow control, or traffic management, where PDE models with varying coefficients are common. By integrating neural operators into the control loop, the work bridges model-based PDE control and data-driven learning, opening a new pathway for efficient, scalable control of distributed parameter systems.