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

arXiv: https://arxiv.org/abs/2502.00043 · HTML: https://mlsanity.com/paper/2502.00043/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 109 references that are in the map.
- First posted on arXiv 27 Jan 2025.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [End-to-End Multi-Task Learning with Attention](https://mlsanity.com/paper/1803.10704/) (2018)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Sequence-to-Sequence Prediction of Vehicle Trajectory via LSTM Encoder-Decoder Architecture](https://mlsanity.com/paper/1802.06338/) (2018)
- [Generalizing Koopman Theory to allow for inputs and control](https://mlsanity.com/paper/1602.07647/) (2016)
- [Dissipation of stop-and-go waves via control of autonomous vehicles: Field experiments](https://mlsanity.com/paper/1705.01693/) (2017)
- [A Physics-Informed Deep Learning Paradigm for Car-Following Models](https://mlsanity.com/paper/2012.13376/) (2020)
- [Deep Neural Networks with Koopman Operators for Modeling and Control of Autonomous Vehicles](https://mlsanity.com/paper/2007.02219/) (2020)
- [A Generative Car-following Model Conditioned On Driving Styles](https://mlsanity.com/paper/2112.05399/) (2021)
- [DeeP-LCC: Data-EnablEd Predictive Leading Cruise Control in Mixed Traffic Flow](https://mlsanity.com/paper/2203.10639/) (2022)
- [Car-Following Models: A Multidisciplinary Review](https://mlsanity.com/paper/2304.07143/) (2023)
- [Enhancing System-Level Safety in Mixed-Autonomy Platoon via Safe Reinforcement Learning](https://mlsanity.com/paper/2401.11148/) (2024)
- [Physically Analyzable AI-Based Nonlinear Platoon Dynamics Modeling During Traffic Oscillation: A Koopman Approach](https://mlsanity.com/paper/2406.14696/) (2024)
- [Smoothing Traffic Flow via Control of Autonomous Vehicles](https://mlsanity.com/paper/1812.09544/) (2018)
- [Knowledge Transfer from Simple to Complex: A Safe and Efficient Reinforcement Learning Framework for Autonomous Driving Decision-Making](https://mlsanity.com/paper/2410.14468/) (2024)
- [Influence of CAV Clustering Strategies on Mixed Traffic Flow Characteristics: An Analysis of Vehicle Trajectory Data](https://mlsanity.com/paper/2003.08290/) (2020)
- [Controllability Analysis and Optimal Control of Mixed Traffic Flow with Human-driven and Autonomous Vehicles](https://mlsanity.com/paper/2002.02099/) (2020)
- [Cooperative Formation of Autonomous Vehicles in Mixed Traffic Flow: Beyond Platooning](https://mlsanity.com/paper/2009.04254/) (2020)
- [Leading Cruise Control in Mixed Traffic Flow: System Modeling, Controllability, and String Stability](https://mlsanity.com/paper/2012.04313/) (2020)
- [Robust Safety for Mixed-Autonomy Traffic with Delays and Disturbances](https://mlsanity.com/paper/2310.04007/) (2023)
- [Decentralized Robust Data-driven Predictive Control for Smoothing Mixed Traffic Flow](https://mlsanity.com/paper/2401.15826/) (2024)
- [Mitigating Stop-and-Go Traffic Congestion with Operator Learning](https://mlsanity.com/paper/2411.05866/) (2024)
- [Distributed data-driven predictive control for cooperatively smoothing mixed traffic flow](https://mlsanity.com/paper/2210.13171/) (2022)
- [Incorporating lane-change prediction into energy-efficient speed control of connected autonomous vehicles at intersections](https://mlsanity.com/paper/2407.15004/) (2024)

## Abstract (arXiv)

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.