Mitigating Traffic Oscillations in Mixed Traffic Flow with Scalable Deep Koopman Predictive Control

Mitigating traffic oscillations in mixed flows of connected automated vehicles (CAVs) and human-driven vehicles (HDVs) is critical for enhancing traffic stability. A key challenge lies in modeling the nonlinear, heterogeneous behaviors of HDVs within computationally tractable predictive control frameworks. This study proposes an adaptive deep Koopman predictive control framework (AdapKoopPC) to address this issue. The framework features a novel deep Koopman network, AdapKoopnet, which represents complex HDV car-following dynamics as a linear system in a high-dimensional space by adaptively learning from naturalistic data. This learned linear representation is then embedded into a Model Predictive Control (MPC) scheme, enabling real-time, scalable, and optimal control of CAVs. We validate our framework using the HighD dataset and extensive numerical simulations. Results demonstrate that AdapKoopnet achieves superior trajectory prediction accuracy over baseline models. Furthermore, the complete AdapKoopPC controller significantly dampens traffic oscillations with lower computational cost, exhibiting strong performance even at low CAV penetration rates. The proposed framework offers a scalable and data-driven solution for enhancing stability in realistic mixed traffic environments. The code is made publicly available.