# Constrained Optimal Fuel Consumption of HEVs under Observational Noise

arXiv: https://arxiv.org/abs/2410.20913 · HTML: https://mlsanity.com/paper/2410.20913/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 43 references that are in the map.
- First posted on arXiv 28 Oct 2024.

## Builds on (most cited first, 19 of 19)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [Responsive Safety in Reinforcement Learning by PID Lagrangian Methods](https://mlsanity.com/paper/2007.03964/) (2020)
- [A Lyapunov-based Approach to Safe Reinforcement Learning](https://mlsanity.com/paper/1805.07708/) (2018)
- [Robust Deep Reinforcement Learning against Adversarial Perturbations on State Observations](https://mlsanity.com/paper/2003.08938/) (2020)
- [Maximum Entropy RL (Provably) Solves Some Robust RL Problems](https://mlsanity.com/paper/2103.06257/) (2021)
- [Action Robust Reinforcement Learning and Applications in Continuous Control](https://mlsanity.com/paper/1901.09184/) (2019)
- [Robust Deep Reinforcement Learning with Adversarial Attacks](https://mlsanity.com/paper/1712.03632/) (2017)
- [Robust Reinforcement Learning on State Observations with Learned Optimal Adversary](https://mlsanity.com/paper/2101.08452/) (2021)
- [Reinforcement Learning with Perturbed Rewards](https://mlsanity.com/paper/1810.01032/) (2018)
- [Constrained Variational Policy Optimization for Safe Reinforcement Learning](https://mlsanity.com/paper/2201.11927/) (2022)
- [Efficient Adversarial Training without Attacking: Worst-Case-Aware Robust Reinforcement Learning](https://mlsanity.com/paper/2210.05927/) (2022)
- [On the Robustness of Safe Reinforcement Learning under Observational Perturbations](https://mlsanity.com/paper/2205.14691/) (2022)
- [Model-based Adversarial Meta-Reinforcement Learning](https://mlsanity.com/paper/2006.08875/) (2020)
- [Robust Reinforcement Learning as a Stackelberg Game via Adaptively-Regularized Adversarial Training](https://mlsanity.com/paper/2202.09514/) (2022)
- [Safe Reinforcement Learning with Dual Robustness](https://mlsanity.com/paper/2309.06835/) (2023)
- [Constrained Optimal Fuel Consumption of HEV: A Constrained Reinforcement Learning Approach](https://mlsanity.com/paper/2403.07503/) (2024)

## Abstract (arXiv)

In our prior work, we investigated the minimum fuel consumption of a hybrid electric vehicle (HEV) under a state-of-charge (SOC) balance constraint, assuming perfect SOC measurements and accurate reference speed profiles. The constrained optimal fuel consumption (COFC) problem was addressed using a constrained reinforcement learning (CRL) framework. However, in real-world scenarios, SOC readings are often corrupted by sensor noise, and reference speeds may deviate from actual driving conditions. To account for these imperfections, this study reformulates the COFC problem by explicitly incorporating observational noise in both SOC and reference speed. We adopt a robust CRL approach, where the noise is modeled as a uniform distribution, and employ a structured training procedure to ensure stability. The proposed method is evaluated through simulations on the Toyota Prius hybrid system (THS), using both the New European Driving Cycle (NEDC) and the Worldwide Harmonized Light Vehicles Test Cycle (WLTC). Results show that fuel consumption and SOC constraint satisfaction remain robust across varying noise levels. Furthermore, the analysis reveals that observational noise in SOC and speed can impact fuel consumption to different extents. To the best of our knowledge, this is the first study to explicitly examine how observational noise -- commonly encountered in dynamometer testing and predictive energy control (PEC) applications -- affects constrained optimal fuel consumption in HEVs.