Closed-form solution to the dynamic programming for a heavy-duty parallel hybrid vehicle energy management

Dynamic programming (DP) is frequently used to obtain the optimal solution to the hybrid electric vehicle (HEV) energy management. The trade-off between the accuracy and the computational effort is the biggest problem for the DP method. The closed-form solution to the DP is proposed to solve this problem. Firstly, the affine linear model of the engine fuel rate is obtained based on engine test data. The piecewise linear approximation of the motor power demand is obtained considering the different energy flows in the charging and discharging stages of the battery. Then, the second-order Taylor expansion for the cost matrix at each time and state grid point is introduced to get the closed-form solution of the optimal torque split. The results show that this method can greatly reduce the computing burden by 93% while ensuring near-optimal fuel economy compared with the conventional DP method.