  This paper introduces a novel approach to PDE boundary control design using
neural operators to alleviate stop-and-go instabilities in congested traffic
flow. Our framework leverages neural operators to design control strategies for
traffic flow systems. The traffic dynamics are described by the Aw-Rascle-Zhang
(ARZ) model, which comprises a set of second-order coupled hyperbolic partial
differential equations (PDEs). Backstepping method is widely used for boundary
control of such PDE systems. The PDE model-based control design can be
time-consuming and require intensive depth of expertise since it involves
constructing and solving backstepping control kernels. To overcome these
challenges, we present two distinct neural operator (NO) learning schemes aimed
at stabilizing the traffic PDE system. The first scheme embeds NO-approximated
gain kernels within a predefined backstepping controller, while the second one
directly learns a boundary control law. The Lyapunov analysis is conducted to
evaluate the stability of the NO-approximated gain kernels and control law. It
is proved that the NO-based closed-loop system is practical stable under
certain approximation accuracy conditions in NO-learning. To validate the
efficacy of the proposed approach, simulations are conducted to compare the
performance of the two neural operator controllers with a PDE backstepping
controller and a Proportional Integral (PI) controller. While the
NO-approximated methods exhibit higher errors compared to the backstepping
controller, they consistently outperform the PI controller, demonstrating
faster computation speeds across all scenarios. This result suggests that
neural operators can significantly expedite and simplify the process of
obtaining boundary controllers in traffic PDE systems.
