Gaussian Process Approximate Dynamic Programming for Energy-Optimal Supervisory Control of Parallel Hybrid Electric Vehicles

We propose an energy-efficient supervisory control method for the power management of parallel hybrid electric vehicles (HEVs) to improve the fuel economy and reduce exhaust gas emissions. Plug-in HEVs ((P)HEVs) have multiple power sources (e.g., an engine and motor) that should be cooperatively operated to meet the required instantaneous traction power for the desired vehicle speed while satisfying their physical limits. Because the efficiencies of the engine and motor vary with different operating speeds and torques, the main issue of energy-efficient power management is to allocate the power demand among the power sources by achieving maximum power conversion efficiencies and satisfy the operating limits. For an efficient power allocation, an optimal control problem is formulated, and a global solution is found through deterministic dynamic programming (DP). Owing to the curse of dimensionality and uncertainties in real driving, DP solutions are not directly applicable in real time. To resolve the limitations of DP, we employ a non-parametric Bayesian function approximation technique using a Gaussian process (GP). The offline DP solutions obtained from a set of real vehicle driving test data were used to learn a state-dependent probabilistic value function through Gaussian process regression. For online implementations, a receding horizon control scheme was applied for the feedback control of the power management. In comparison with the existing charge sustaining strategy and charge depleting and charge sustaining mixed controllers, we recorded fuel efficiency improvements of over 4.8% and 7.3%, respectively, in a mixed urban-suburban route.