Robust Modeling for Optimal Control of Parallel Hybrids With Dynamic Programming

The aim of this work is to provide insight and guidelines for engineers and researchers when developing hybrid powertrain models to be employed in a dynamic programming optimal control algorithm. In particular, we focus on the advantages and disadvantages of the various control sets that can be used to characterize the power flow (e.g. the engine torque or a torque-split coefficient). Dynamic programming is the reference optimal control technique for hybrid electric vehicles. However, its practical implementation is not exempt from numerical issues which may hamper its accuracy. Amongst these, some are directly related to the different modeling choices that can be made when defining the system dynamics of the powertrain. To treat these issues, we first define four relevant evaluation criteria: control bounds definition, numerical efficiency, model complexity and interpretability. Then, we introduce eight different control sets and we discuss and compare them in light of these criteria. This discussion is supported by an extensive set of numerical experiments on a p2 parallel hybrid. Finally, we revisit our analysis and simulation results to draw modeling recommendations.