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Dynamic programming (DP) is currently the reference optimal energy management approach for hybrid electric vehicles (HEVs). However, several research concerns arise regarding the effective application of DP for optimal HEV control problems which involve a significant number of control variables, state variables and optimization constraints. This paper deals with an optimal control problem for a full parallel P2 HEV with constraints on battery state-of-charge (SOC), battery lifetime in terms of state-of-health (SOH), and smooth driving in terms of the frequencies of internal combustion engine (ICE) activations and gear shifts over time. The DP formulation for the considered HEV control problem is outlined, yet its practical application is demonstrated as unfeasible due to a lack of computational power and memory in current desktop computers. To overcome this drawback, a computationally efficient version of DP is proposed which is named Slope-weighted Rapid Dynamic Programming (SRDP). Computational advantage is achieved by SRDP in considering only the most efficient HEV powertrain operating points rather than the full set of control variable values at each time instant of the drive cycle. A benchmark study simulating various drive cycles demonstrates that the introduced SRDP can achieve compliance with imposed control constraints on battery SOC, battery SOH and smooth driving. At the same time, SRDP can achieve up to 78% computational time saving compared with a baseline DP approach considering the Worldwide Harmonized Light Vehicle Test Procedure (WLTP). On the other hand, the increase in the fuel consumption estimated by SRDP is limited within 3.3% compared with the baseline DP approach if the US06 Supplemental Federal Test Procedure is considered. SRDP could thus be exploited to efficiently explore the large design space associated to HEV powertrains.

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Dynamic Programming Based Rapid Energy Management of Hybrid Electric Vehicles with Constraints on Smooth Driving, Battery State-of-Charge and Battery State-of-Health