## Model Predictive Control of a Parallel Plug-In Hybrid Electric Vehicle Relying on Dynamic Programming and Extended Backward-Looking Model

*IEEE Transactions on Control Systems Technology, Vol. 32, No. 2, pp. 581-594*,

*2024*.

This article presents the design of a model predictive control (MPC) strategy for power flow management of a plug-in hybrid electric vehicle (PHEV), given in P2 parallel configuration and operating in a charge sustaining (CS) mode. The strategy relies on vehicle velocity prediction, a backward-looking (BWD) powertrain prediction model extended with transient loss effects, and dynamic programming (DP)-based control variable optimization on receding time horizon. The extended BWD (EXT-BWD) model accounts for power and torque losses occurring during powertrain transients, such as those related to gear shifting, engine-ON events, and dog clutch synchronization. The DP-minimized MPC cost function reflects the fuel consumption over the receding time horizon and the remaining trip time window. The latter allows for specifying the battery state-of-charge (SoC) directly at the end of driving cycle and avoiding tuning of cost function weighting coefficients that are generally dependent on driving cycle. The proposed MPC strategy is first verified against the global benchmark obtained by applying offline DP optimization over the full driving cycle. The MPC strategy is then compared with the previously developed, equivalent consumption minimization strategy (ECMS), given in regular and adaptive forms. The verification results indicate that the proposed MPC strategy is closely approaching the DP benchmark and provides overly consistent fuel savings when compared to both forms of ECMS.