Computationally Efficient Energy Management in Hybrid Electric Vehicles Based on Approximate Pontryagin’s Minimum Principle

Abstract

This article presents an energy management method for a parallel hybrid electric vehicle (HEV) based on approximate Pontryagin’s Minimum Principle (A-PMP). The A-PMP optimizes gearshift commands and torque distribution for overall energy efficiency. As a practical numerical solution in PMP, the proposed methodology utilizes a piecewise linear approximation of the engine fuel rate and state of charge (SOC) derivative by considering drivability and fuel economy simultaneously. Moreover, battery aging is explicitly studied by introducing a control-oriented model, which aims to investigate the effect of battery aging on the optimization performance in the development of the HEVs. An approximate energy management strategy with piecewise linear models is then formulated by the A-PMP, which targets a better performance for the Hamiltonian optimization. The gearshift map is extracted from the optimal results in the standard PMP to hinder frequent gearshift by considering both drivability and fuel economy. Utilizing an approximated Hamilton function, the torque distribution, gearshift command, and the battery aging degradation are jointly optimized under a unified framework. Simulations are performed for dynamic programming (DP), PMP, and A-PMP to validate the effectiveness of the proposed approach. The results indicate that the proposed methodology achieves a close fuel economy compared with the DP-based optimal solution. Moreover, it improves the computation efficiency by 50% and energy saving by 3.5%, compared with the PMP, while ensuring good drivability and fuel efficiency.

Real-Time Energy Management Strategy of Hydrogen Fuel Cell Hybrid Electric Vehicles Based on Power Following Strategy–Fuzzy Logic Control Strategy Hybrid Control

“…high computational effort and poor real-time performance. control strategies based on transient optimisation [13][14][15]. realise real-time optimal control with good control effect.…”

“…The instantaneous optimisation strategy solves the optimisation problem using an instantaneous minimisation of the hydrogen consumption cost function, which is updated in real time. The equivalent consumption minimisation strategy (ECMS) [13] and Pontryagin's minimum principle (PMP) [14,15] can approximate the global optimal solution by appropriately simplifying the whole vehicle model and selecting the appropriate equivalence coefficients. However, this method requires the precise selection of equivalence coefficients and construction of the corresponding prediction model, which are computationally complex and not easy for real-time applications.…”

Optimization and cutting‐edge design of fuel‐cell hybrid electric vehicles

“…Real‐time and approximately optimal EMS based on the PMP can control the SOC of the battery within a certain range and determine the approximately optimal hydrogen consumption, thereby improving FC durability and reducing the average daily operating cost 171 . To lower the average daily running cost and improve the FC life, a real‐time EMS based on the PMP that considers the fuel efficiency and power source durability has been introduced 172 . The ECMS has been demonstrated to boost fuel economy and prolong the battery life of the FCHEV by simulation on the ADVISOR and Simulink 173 .…”

Optimal Control Strategy for Parallel Plug-in Hybrid Electric Vehicles Based on Dynamic Programming

“…Li et al [11] proposed to integrate the fuzzy inference system (FIS) for online reference SOC estimation and the adaptive update law with a flow recognition function into the main framework of the adaptive equivalent power consumption minimization strategy (A-ECMS). Zhang et al [12] proposed an energy management method based on an approximate Pontryagin's minimum principle (A-PMP), which uses the approximate Hamiltonian function to jointly optimize the torque distribution, shift command, and battery aging performance under the approximate PMP framework. Although the real-time optimization control algorithm ignores the influence of many conditions, such as driving condition and mileage, the control effect of the algorithm is not as good as that of the global optimal algorithm.…”