This paper presents a novel method to solve the energy management problem for hybrid electric vehicles (HEVs) with engine start and gearshift costs. The method is based on a combination of deterministic dynamic programming (DP) and convex optimization. As demonstrated in a case study, the method yields globally optimal results while returning the solution in much less time than the conventional DP method. In addition, the proposed method handles state constraints, which allows for the application to scenarios where the battery state of charge (SOC) reaches its boundaries.

a b s t r a c tA benchmark control problem was developed for a special session of the IFAC Workshop on Engine and Powertrain Control, Simulation and Modeling (E-COSM 12), held in Rueil-Malmaison, France, in October 2012. The online energy management of a plug-in hybrid-electric vehicle was to be developed by the benchmark participants. The simulator, provided by the benchmark organizers, implements a model of the GM Voltec powertrain. Each solution was evaluated according to several metrics, comprising of energy and fuel economy on two driving profiles unknown to the participants, acceleration and braking performance, computational performance. The nine solutions received are analyzed in terms of the control technique adopted (heuristic rule-based energy management vs. equivalent consumption minimization strategies, ECMS), battery discharge strategy (charge depleting-charge sustaining vs. blended mode), ECMS implementation (vector-based vs. map-based), ways to improve the implementation and improve the computational performance. The solution having achieved the best combined score is compared with a global optimal solution calculated offline using the Pontryagin's minimum principlederived optimization tool HOT.

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Motivated by the fact that the real driving NO x emissions (RDE) of conventional diesel vehicles can exceed the legislation norms by far, a concept for the control of RDE with a diesel parallel hybrid electric vehicle (HEV) is proposed. By extending the well-known equivalent consumption minimization strategy (ECMS), the power split degree of freedom is used to control the NO x emissions and the battery state of charge (SOC) simultaneously. Through an appropriate formulation of the problem, the feedback control is shown to be separable into two dependent PI controllers. By hardware-in-the-loop (HIL) experiments, as well as by simulations, the proposed method is shown to minimize the fuel consumption while tracking a given reference trajectory for both the NO x emissions and the battery SOC.

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