Co-State Variable Determination in Pontryagin’s Minimum Principle for Energy Management of Hybrid Vehicles

Jianxing Zhang, Chunhua Zheng, Suk Won Cha, Shanxu Duan


In order to achieve the best fuel economy for hybrid vehicles, energy management strategies should optimize the power allocation between power sources. Recently, Pontryagin’s Minimum Principle (PMP) has been attracting attention for the energy management of hybrid vehicles owing to the solution optimality and the calculation instantaneity. In the PMP, there is an important control parameter, which is defined as the co-state variable and difficult to be determined. This research mainly deals with the co-state variable, where the PMP is applied to a fuel cell hybrid vehicle (FCHV) and a hybrid electric vehicle (HEV) respectively, and the effect of the co-state variable on the optimal solution is discussed for each case. The determination of the co-state variable for the cases of certain driving cycles and uncertain driving cycles is discussed, and an online co-state variable updating method is proposed for the uncertain driving cycle cases and its effectiveness is proved.