Learning Optimal Robust Control for Nonlinear Mixed Traffic Under External Disturbance

The integration of connected and automated vehicles (CAVs) into traffic systems holds potential to mitigate undesired disturbances. Nevertheless, coexisting human-driven vehicles (HDVs) introduce complex behavioral disturbances, which has imposed critical challenges for control robustness. This study develops a computational framework based on policy iteration to derive robust control policies with optimized attenuation performance for nonlinear mixed traffic flow. Specifically, robust$H_{\infty }$control problem is solved by applying the framework of zero-sum game, whose solution at the Nash equilibrium is transformed into a Hamilton–Jacobi (HJ) inequality with a Hamiltonian constraint. For achieving desired attenuation performance, the value function is updated by gradient descent based on counterexamples violating Hamiltonian and monotonicity constraints, where the positive definiteness of the value function is ensured by convex neural networks, facilitating the analysis of control stability via Lyapunov methods. By utilizing constraint gaps, the attenuation level is optimized through the analytical formulae derived from the HJ inequality. The stability and algorithm convergence are proved. Experimental results demonstrate the capability of the learned controller to effectively attenuate disturbance propagation and stabilize mixed traffic flow.