Physics-Informed Predictive Energy Management Strategy for HEVs Using Kalman-Enhanced Transformer

Predictive energy management strategies (PEMSs) have attracted increasing attention in hybrid electric vehicles (HEVs) for improving fuel economy and powertrain efficiency using anticipated driving information. For PEMS, data-driven velocity prediction is widely used to capture complex driving patterns from historical trajectories and future traffic priors, but often lacks kinematic awareness, leading to physical causality violations and long-horizon state drift. To address these issues, this paper proposes a physics-informed PEMS, where a Physics-Informed Spatio-Temporal Network (PI-STN) provides control-oriented velocity information for an MPC-based energy management controller. Specifically, to address pseudo-motion in velocity prediction under standstill conditions, a global zero-speed gating mechanism is introduced; to suppress acceleration/deceleration trends that violate vehicle kinematic causality, a causal penalty is designed; and to mitigate temporal phase misalignment between data-driven predictions and physical motion priors, a Differentiable Kalman Filter (DKF) is incorporated. At each receding horizon step, the PI-STN-predicted velocity sequence is converted into future power demand through longitudinal vehicle dynamics and used by MPC for engine–battery power allocation under SOC and engine transient constraints. Under the same tested conditions, the proposed strategy reduces engine power fluctuation by 15.1% compared with BiLSTM-Transformer, and achieves an equivalent fuel consumption of 323.74 g, outperforming Transformer-KF by 3.12%.