Cubic Spline Approximations of the Dynamic Programming Value Function in HEV Energy Management Problems

Other conference contribution, 2013

Energy management of a hybrid electric powertrain is a non-linear and mixed integer optimization problem that often is solved with Dynamic Programming (DP); thus requiring the problem to be gridded both in time, control signals and the states. To ensure a high accuracy of the solution the grid must be dense, meaning that the resulting value function can require several megabytes of memory. The first contribution of the paper is therefore a sensitivity study where the effect of a sparsely gridded state is investigated, both for a hybrid electric vehicle (HEV) and a plug-in HEV (PHEV). The study shows that it is possible to use a sparse grid for an HEV, but not for a PHEV. The second contribution is a method to approximate the DP value function with cubic splines. The results indicate that it is possible to use only a few splines, if the knot points are determined based on the characteristics of the value function. Thereby it is possible to significantly reduce the memory requirements of the PHEV value function, without any noticeable increase in fuel consumption.