  Connected and automated vehicles (CAVs) technologies promise to attenuate
undesired traffic disturbances. However, in mixed traffic where human-driven
vehicles (HDVs) also exist, the nonlinear human-driving behavior has brought
critical challenges for effective CAV control. This paper employs the policy
iteration method to learn the optimal robust controller for nonlinear mixed
traffic systems. Precisely, we consider the H_infty control framework and
formulate it as a zero-sum game, the equivalent condition for whose solution is
converted into a Hamilton-Jacobi inequality with a Hamiltonian constraint.
Then, a policy iteration algorithm is designed to generate stabilizing
controllers with desired attenuation performance. Based on the updated robust
controller, the attenuation level is further optimized in sum of squares
program by leveraging the gap of the Hamiltonian constraint. Simulation studies
verify that the obtained controller enables the CAVs to dampen traffic
perturbations and smooth traffic flow.
