We assume accurate observation of battery state of charge (SOC) and precise speed curves when addressing the constrained optimal fuel consumption (COFC) problem via constrained reinforcement learning (CRL). However, in practice, SOC measurements are often distorted by noise or confidentiality protocols, and actual reference speeds may deviate from expectations. We aim to minimize fuel consumption while maintaining SOC balance under observational perturbations in SOC and speed. This work first worldwide uses seven training approaches to solve the COFC problem under five types of perturbations, including one based on a uniform distribution, one designed to maximize rewards, one aimed at maximizing costs, and one along with its improved version that seeks to decrease reward on Toyota Hybrid Systems (THS) under New European Driving Cycle (NEDC) condition. The result verifies that the six can successfully solve the COFC problem under observational perturbations, and we further compare the robustness and safety of these training approaches and analyze their impact on optimal fuel consumption.
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