Analytic Solutions to the Dynamic Programming Subproblem in Hybrid Vehicle Energy Management

The computationally demanding dynamic programming (DP) algorithm is frequently used in academic research to solve the energy management problem of a hybrid electric vehicle (HEV). This paper is exclusively focused on how the computational demand of such a computation can be reduced. The main idea is to use a local approximation of the gridded cost-to-go and derive an analytic solution for the optimal torque split decision at each point in the time and state grid. Thereby, it is not necessary to quantize the torque split and identify the optimal decision by interpolating in the cost-to-go. Two different approximations of the cost-to-go are considered in this paper: 1) a local linear approximation and 2) a quadratic spline approximation. The results indicate that computation time can be reduced by orders of magnitude with only a slight degradation in simulated fuel economy. Furthermore, with a spline approximated cost-to-go, it is also possible to significantly reduce the memory storage requirements. A parallel plug-in HEV is considered in this paper, but the method is also applicable to an HEV.