Real-time economic following velocity and gear planning for commercial vehicles based on the bi-level optimization

Current Predictive Adaptive Cruise Control (PACC) systems pose significant challenges. These include poor collaborative optimisation between economic velocity and the powertrain system, conservative energy-saving strategies and underutilisation of map data due to real-time constraints. A computationally efficient collaborative optimisation method is proposed for economic following velocity and gear shifting based on Bi-level optimisation theory. Based on the Bi-level theory, economic following velocity and gear shifting are decoupled and hierarchically planned. The lower-level subproblem constructs the objective function based on a dynamic-weight safety distance model within the Model Predictive Control (MPC) framework, solving the economic following velocity by the Continuous Generalized Minimal Residual Method (C/GMRES). The upper-level subproblem solves the economic gear shifting by the optimal control law based on the economic following velocity. Finally, comparative experiments are conducted between the proposed PACC algorithm, a standard Adaptive Cruise Control (ACC) algorithm, and a benchmark Dynamic Programming-Model Predictive Control (DP-MPC) PACC algorithm. The results show that the proposed PACC algorithm reduces fuel consumption by approximately 5.76% compared to the ACC. Compared to the benchmark algorithm, the proposed PACC algorithm also demonstrates significantly improved computational efficiency while achieving comparable energy savings.