Optimal Control of the Gearshift Command for Hybrid Electric Vehicles

This paper proposes a design method for the energy management strategy to explore the potential fuel saving of a hybrid electric vehicle (HEV) equipped with an automated manual transmission. The control algorithm is developed based on the combination of dynamic programming (DP) and Pontryagin´s minimum principle (PMP) to optimally control the discrete gearshift command, in addition to the continuous power split between the internal combustion engine and the electric machine. The proposed method outperforms DP in terms of computational efficiency, being 171 times faster, without loss of accuracy. Simulation results for a middle-sized HEV on the New European Drive Cycle show that, to further optimize the gearshift strategy, an additional fuel saving of 20.3% can be reached. Furthermore, with the start-stop functionality available, it is shown that the two-point boundary-value problem following from PMP cannot be solved with sufficient accuracy without loss of optimality. This means that the finding of a constant value for the Lagrange multiplier while satisfying the battery state-of-energy (SOE) at the terminal time is not always guaranteed. Therefore, an alternative approach of SOE feedback control to adapt the Lagrange multiplier is adopted. The obtained results are very close to the globally optimal solution from DP. Simulation results, including the start-stop functionality, show that the relative fuel saving can be up to 26.8% compared with the case of a standard gearshift strategy.