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Hybrid technologies enable the reduction of noxious tailpipe emissions and conformance with ever-decreasing allowable homologation limits. The complexity of the hybrid powertrain technology leads to an energy management problem with multiple energy sinks and sources comprising the system resulting in a high-dimensional time dependent problem for which many solutions have been proposed. Methods that rely on accurate predictions of potential vehicle operations are demonstrably more optimal when compared to rule-based methodology [1]. In this paper, a previously proposed energy management strategy based on an offline optimization using dynamic programming is investigated. This is then coupled with an online model predictive control strategy to follow the predetermined optimal battery state of charge trajectory prescribed by the dynamic program.

The energy consumption of a vehicle is typically determined either by testing or in simulation. While both approaches are valid, they only work for a specific drive cycle, they are time intensive, and they do not directly result in a closed-form relationship between key parameters and consumption. This paper presents an alternative approach that determines the consumption based on a simple analytical model of the vehicle and statistical parameters of the drive cycle, specifically the moments of the velocity. This results in a closed-form solution that can be used for analysis or synthesis. The drive cycle is quantified via its moments, specifically the average speed, the standard deviation of the speed as well as the higher order moments skewness, and the kurtosis. A mixed quadratic term is added to account for acceleration or aggressiveness, but it is noticeably distinct from the conventional metric of positive kinetic energy (PKE).

Hybrid electric vehicles offer significant fuel economy benefits, because battery and fuel can be used as complementing energy sources. This paper presents the use of dynamic programming to find the optimal blend of power sources, leading to the lowest fuel consumption and the lowest level of harmful emissions. It is found that the optimal engine behavior differs substantially to an on-line adaptive control system previously designed for the Lotus Evora 414E. When analyzing the trade-off between emission and fuel consumption, CO and HC emissions show a traditional Pareto curve, whereas NOx emissions show a near linear relationship with a high penalty. These global optimization results are not directly applicable for online control, but they can guide the design of a more efficient hybrid control system.