Energy Management of Hybrid Electric Commercial Vehicles Based on Neural Network-Optimized Model Predictive Control

Energy management for hybrid electric commercial vehicles, involving continuous power output and discrete gear shifting, constitutes a typical mixed-integer programming (MIP) problem, presenting significant challenges for real-time performance and computational efficiency. To address this, this paper proposes a physics-informed neural network-optimized model predictive control (PINN-MPC) strategy. On one hand, this strategy simultaneously optimizes continuous and discrete states within the MPC framework to achieve the integrated objectives of minimizing fuel consumption, tracking speed, and managing battery state-of-charge (SOC). On the other hand, to overcome the prohibitively long solving time of the MIP-MPC, a physics-informed neural network (PINN) optimizer is designed. This optimizer employs the soft-argmax function to handle discrete gear variables and embeds system dynamics constraints using an augmented Lagrangian approach. Validated via hardware-in-the-loop (HIL) testing under two distinct real-world driving cycles, the results demonstrate that, compared to the open-source solver BONMIN, PINN-MPC significantly reduces computation time—dramatically decreasing the average solving time from approximately 10 s to about 5 ms—without sacrificing the combined vehicle dynamic and economic performance.