Proximal data-driven predictive control with nonsmooth dynamics for eco-smoothing mixed traffic

Anticipative and predictive control of connected and automated vehicles (CAVs) holds significant promise for improving vehicle-level performance while smoothing traffic flow in mixed traffic. Recent studies have therefore increasingly explored predictive and connected cruise control strategies, with primary emphasis on either vehicle-level performance or traffic-flow operation. Nevertheless, these two research directions have been largely pursued in parallel, with limited attention paid to frameworks that use downstream traffic information to directly inform vehicle-level optimization and thereby address eco-driving and traffic-oscillation attenuation within a single real-time control formulation. Moreover, stop-and-go traffic waves induce frequent traction-regeneration transitions in electrified vehicles, thereby inevitably introducing nonsmooth powertrain dynamics and further complicating real-time implementation. To address these challenges, this paper proposes a proximal data-driven predictive control framework for CAVs in mixed traffic, which optimizes vehicle-level eco-driving while implicitly promoting local traffic-flow smoothing under lean connectivity through the combined effects of vehicle-level objective design and look-ahead traffic prediction, with nonsmooth electrified vehicle dynamics explicitly incorporated into the control formulation. A non-parametric data-driven predictor is developed to estimate the future motion of the preceding traffic under lean connectivity, leveraging downstream traffic information from a distant connected human-driven vehicle (CHV). To enable efficient gradient-based optimization, the nonsmooth dynamics arising from asymmetric traction-regeneration efficiencies are regularized via Lasry–Lions double envelopes, yielding a smooth surrogate that preserves the physical characteristics. Based on the resulting formulation, a tailored real-time solution algorithm, PANDA ( P roximal A veraged quasi- N ewton with a D aptive linesearch A lgorithm), is developed to solve the nonlinear optimal control problem in a fast and memory-efficient way. Simulation results demonstrate that the proposed strategy with highly anticipative driving behavior effectively suppresses traffic oscillations, and reduces vehicle-level and traffic-level energy consumption by 22.69% and 30.63% in an open-boundary straight road scenario, and by 53.31% and 54.25% in a severe closed-boundary ring road scenario where traffic oscillations cannot dissipate through boundary effects, while maintaining computational performance suitable for embedded applications.