An adaptive co-state design method for PMP-based energy management of plug-in hybrid electric vehicles based on fuzzy logical control

The determination of the optimal co-state in Pontryagin's minimum principle-based (PMP-based) energy management strategy (EMS) in real-time remains a significant challenge. This paper proposes a fuzzy logic-based approach to tackle this problem. Firstly, an offline optimization method based on the multi-island genetic algorithm (MIGA) is proposed to calculate the optimal co-state of the PMP-based EMS for a plug-in hybrid electric vehicle (PHEV) based on the provided driving cycles. Secondly, a comprehensive evaluation of the influence on the optimal co-state is conducted based on the vehicle's velocity and load, utilizing real-life and representative driving scenarios. Subsequently, a fuzzy logic-based controller is formulated for online modification of the co-state, with inputs including vehicle velocity, load, and acceleration. Finally, the proposed method is evaluated against benchmarks including dynamic programming (DP), charge-depleting and charge-sustaining (CD-CS), and PMP-constant solutions using nine actual driving cycles. The findings demonstrate that the controller with the fuzzy logic method displays significant adaptability to diverse driving cycles. The proposed PMP-adaptive strategy exhibits significant improvement compared to CD-CS, with energy-saving effectiveness approaching DP solutions. In addition, the computational efficiency of the PMP-adaptive is superior to that of the CD-CS, which presents a valuable advantage for real-time applications. •The MIGA was introduced to optimize the co-state, addressing the issue of initial co-state assignment during solving.•The impact on the co-state was analyzed, and the influence of load and velocity on the optimal co-state was elucidated.•An adaptive co-state design framework was developed using fuzzy logical control considering velocity, load, and acceleration.