Hybrid electric vehicles (HEVs) are becoming increasingly popular because
they can better combine the working characteristics of internal combustion
engines and electric motors. However, the minimum fuel consumption of an HEV
for a battery electrical balance case under a specific assembly condition and a
specific speed curve still needs to be clarified in academia and industry.
Regarding this problem, this work provides the mathematical expression of
constrained optimal fuel consumption (COFC) from the perspective of constrained
reinforcement learning (CRL) for the first time globally. Also, two mainstream
approaches of CRL, constrained variational policy optimization (CVPO) and
Lagrangian-based approaches, are utilized for the first time to obtain the
vehicle's minimum fuel consumption under the battery electrical balance
condition. We conduct case studies on the well-known Prius TOYOTA hybrid system
(THS) under the NEDC condition; we give vital steps to implement CRL approaches
and compare the performance between the CVPO and Lagrangian-based approaches.
Our case study found that CVPO and Lagrangian-based approaches can obtain the
lowest fuel consumption while maintaining the SOC balance constraint. The CVPO
approach converges stable, but the Lagrangian-based approach can obtain the
lowest fuel consumption at 3.95 L/100km, though with more significant
oscillations. This result verifies the effectiveness of our proposed CRL
approaches to the COFC problem.

混合动力汽车是越来越受欢迎，因为它们可以更好地结合内燃机和电动机的工作特性。本文首次从有限增强学习的角度提供了有限约束优化燃料消耗（COFC）的数学表达式，并首次利用有限变分策略优化（CVPO）和基于 Lagrange 方法的有限方法来获得混合动力汽车在电池电力平衡条件下的最小燃料消耗。通过对著名的 Prius TOYOTA 混合动力系统（THS）在 NEDC 条件下进行案例研究，我们得出了实施 CRL 方法的关键步骤，并比较了 CVPO 和基于 Lagrange 方法之间的性能。我们的案例研究发现 CVPO 和基于 Lagrange 方法在保持 SOC 平衡约束的同时可以获得最低燃料消耗，其中 CVPO 方法收敛稳定，而基于 Lagrange 方法可以获得最低燃料消耗为 3.95 升 / 百公里，尽管有更明显的振荡。这个结果验证了我们提出的 CRL 方法对 COFC 问题的有效性。