In this study, dynamic particle swarm optimization was used to develop optimal strategies for two-variable energy management and gear-shifting in hybrid electric vehicles. To perform simulations, six mathematical subsystems, including a spark ignition engine, lithium battery module, traction motor, automatic manual transmission, longitudinal vehicle dynamics, and driver model were constructed. The control strategies for energy management and gear-shifting were modeled using a dynamic particle swarm optimization strategy with three inputs (i.e., battery state-of-charge, engine speed, and demanded torque) and two outputs (i.e., power-split ratio and gear number). The optimization process was divided into six sequential steps. Four different cases were selected for comparison. The results demonstrate that compared with the baseline case, the improvements in the equivalent fuel and energy consumed in the two-variable optimization case were 30.75% and 59.55%, respectively, during the standard European city driving cycle, and 20.54% and 46.95%, respectively, during the federal test procedure cycle. Consequently, the proposed optimization strategy brought superior performance when applied to hybrid energy management and transmission control. The results of a hardware-in-the-loop verification also confirm the effective performance of proposed the online control. In future work, tests using a real vehicle will be conducted.
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