An Iterative and Hierarchical Approach to Co-optimizing the Velocity Profile and Power-split of Plug-in Hybrid Electric Vehicles

This paper investigates the additional fuel economy benefits with the direct fuel consumption minimization by co-optimizing the vehicle-following and the hybrid powertrain subsystem in a centralized manner upon sequentially optimizing the two subsystems in our previous work [1] (acceleration minimization followed by power-split optimization). However, challenges exist in obtaining the numerical solution of the co-optimization problem due to the following aspects: (i) a mixed-integer problem structure (engine on/off decision), (ii) the presence of second-order pure state constraints (time-varying position constraints), and (iii) unstable dynamics when representing the vehicle-following dynamics by a double integrator. To resolve these difficulties, we propose an iterative and hierarchical numerical strategy combining the gradient projection (direct method) with the single shooting (indirect method). Single shooting is used to deal with the engine on/off decisions in the power-split optimization, and the gradient projection is used to deal with the unstable dynamics and the state constraints. Notably, simulation results show that the proposed approach can solve the co-optimization problem effectively, and demonstrate an additional 8% fuel consumption reduction on a specific driving cycle (and 4%-12% additional fuel reduction on various driving cycles) compared to the sequential optimization approach.