Neural-Operator Control for Traffic Flow Models with Stochastic Demand

In this paper, we investigated the robust stabilization problem for Aw–Rascle–Zhang (ARZ) traffic systems considering stochastic traffic demand from the upstream boundary represented by a Markov-jumping process. We propose a control law that combines operator learning with the backstepping control method. To enhance computational efficiency, the backstepping kernels used in the control law are approximated by neural operators (NOs). We demonstrate that mean-square exponential stability of the closed-loop system, with a nominal neural operator-approximated backstepping control law, can be achieved through Lyapunov analysis. The theoretical results are validated by numerical simulations.