Dynamic programing (DP) algorithm is frequently utilized in studies to solve the energy management schemes (EMS) of hybrid electric vehicles (HEVs). The results of this method are global optimal but computationally inefficient. This paper proposed a rapid approximate DP (RADP) algorithm to improve the time complexity to solve an off-line EMS for a series-parallel HEVs. The key step is to shorten search domain at each grid point of by calculating constraint variables and check constraints before implement Bellman equation. The results demonstrate the computing time has decreased to 1.6% of conventional DP with a slight increase of fuel consumption. And the control policy trajectories, SOC trajectories, and engine working point distribution of RADP are nearly identical to the DP in two driving missions for heavy vehicles.
WieczorekMLewandowskiM.A mathematical representation of an energy management strategy for hybrid energy storage system in electric vehicle and real time optimization using a genetic algorithm. Appl Energy2017; 192: 222–233.
2.
WangHHuangYKhajepourA.Cyber-physical control for energy management of off-road vehicles with hybrid energy storage systems. IEEE/ASME Trans Mechatron2018; 23: 2609–2618.
3.
XiongRCaoJYuQ.Reinforcement learning-based real-time power management for hybrid energy storage system in the plug-in hybrid electric vehicle. Appl Energy2018; 211: 538–548.
4.
HuXJohannessonLMurgovskiN, et al. Longevity-conscious dimensioning and power management of the hybrid energy storage system in a fuel cell hybrid electric bus. Appl Energy2015; 137: 913–924.
5.
RamadanHSBecherifMClaudeF.Energy management improvement of hybrid electric vehicles via combined GPS/rule-based methodology. IEEE Trans Autom Sci Eng2017; 14: 586–597.
6.
PadmarajanBVMcGordonAJenningsPA.Blended rule-based energy management for PHEV: system structure and strategy. IEEE Trans Vehicular Technol2016; 65: 8757–8762.
7.
TianHWangXLuZ, et al. Adaptive fuzzy logic energy management strategy based on reasonable SOC reference curve for online control of plug-in hybrid electric city bus. IEEE Trans Intell Transp Syst2018; 19: 1607–1617.
8.
KamalEAdouaneL.Intelligent energy management strategy based on artificial neural fuzzy for hybrid vehicle. IEEE Trans Intell Vehicles2018; 3(1): 112–125.
9.
ChenZXiongRCaoJ.Particle swarm optimization-based optimal power management of plug-in hybrid electric vehicles considering uncertain driving conditions. Energy2016; 96: 197–208.
10.
ZhangSXiongR.Adaptive energy management of a plug-in hybrid electric vehicle based on driving pattern recognition and dynamic programming. Appl Energy2015; 155: 68–78.
11.
KamalEAdouaneL.Hierarchical energy optimization strategy and its integrated reliable battery fault management for hybrid hydraulic-electric vehicle. IEEE Trans Vehicular Technol2018; 67: 3740–3754.
12.
LarssonVJohannessonLEgardtB.Analytic solutions to the dynamic programming subproblem in hybrid vehicle energy management. IEEE Trans Vehicular Technol2015; 64: 1458–1467.
13.
PengJHeHXiongR.Rule based energy management strategy for a series–parallel plug-in hybrid electric bus optimized by dynamic programming. Appl Energy2017; 185: 1633–1643.
14.
LiuJChenYLiW, et al. Hybrid-trip-model-based energy management of a PHEV with computation-optimized dynamic programming. IEEE Trans Vehicular Technol2018; 67: 338–353.
15.
XieSHuXXinZ, et al. Pontryagin’s minimum principle based model predictive control of energy management for a plug-in hybrid electric bus. Appl Energy2019; 236: 893–905.
16.
DelpratSHofmanTPaganelliS.Hybrid vehicle energy management: singular optimal control. IEEE Trans Vehicular Technol2017; 66: 9654–9666.
17.
BellmanREDreyfusSE.Applied dynamic programming. Princeton, NJ: Princeton University Press, 2015.
18.
KoYLeeJLeeH.A supervisory control algorithm for a series hybrid vehicle with multiple energy sources. IEEE Trans Vehicular Technol2015; 64: 4942–4953.
19.
GuoLGaoBGaoY, et al. Optimal energy management for HEVs in eco-driving applications using bi-level MPC. IEEE Trans Intell Transp Syst2017; 18: 2153–2162.
20.
YuKYangHTanX, et al. Model predictive control for hybrid electric vehicle platooning using slope information. IEEE Trans Intell Transp Syst2016; 17: 1894–1909.
21.
LiuHLiXWangW, et al. Markov velocity predictor and radial basis function neural network-based real-time energy management strategy for plug-in hybrid electric vehicles. Energy2018; 152: 427–444.
22.
SunCSunFHuX, et al. Integrating traffic velocity data into predictive energy management of plug-in hybrid electric vehicles. In: 2015 American Control Conference (ACC), Chicago, IL, 1–3 July 2015, pp.3267–3272. New York, NY: IEEE.
23.
LiuTHuXLiSE, et al. Reinforcement learning optimized look-ahead energy management of a parallel hybrid electric vehicle. IEEE/ASME Trans Mechatron2017; 22: 1497–1507.
24.
RossiFvan BeekPWalshT.Handbook of Constraint Programming Introduction. Kidlington: Elsevier, 2006.
