A Computationally Lightweight Dynamic Programming Formulation for Hybrid Electric Vehicles

Predicting the fuel economy capability of hybrid electric vehicle (HEV) powertrains by solving the related optimal control problem has been available for a few decades. Dynamic programming (DP) is one of the most popular techniques implemented to this end. Current research aims at integrating further powertrain modeling criteria that improve the fidelity level of the optimal HEV powertrain control behavior predicted by DP, thus corroborating the reliability of the fuel economy assessment. Dedicated methodologies need further development to avoid the curse of dimensionality which is typically associated to DP when increasing the number of control and state variables considered. This paper aims at considerably reducing the overall computational effort required by DP for HEVs by removing the state term associated to the battery state-of-charge (SOC). New opportunities open in this way for considering additional vehicle states, such as internal combustion engine (ICE) dynamics in terms of speed and torque, without incurring the curse of dimensionality for the proposed DP formulation. The computational lightweight DP version finds benchmarking here with the baseline DP that considers the full set of control and state variables. Obtained results demonstrate that the proposed DP formulation can remarkably improve the computational efficiency of the baseline DP formulation. Moreover, the fidelity level of the HEV simulation can be improved by limiting the overall number of ICE activations over time. Thanks to the achieved computational lightweight, the proposed method could thus be exploited to accelerate HEV powertrain design processes and to foster on-board HEV powertrain predictive controllers.