Cubic Spline Approximations of the Dynamic Programming Cost-to-go in HEV Energy Management Problems
Paper in proceeding, 2014

The energy management problem of a hybrid electric vehicle (HEV) is a non-linear and mixed integer optimization problem. The problem can be solved with Dynamic Programming (DP), but the algorithm requires the problem to be gridded in time, states and control signals. To ensure a high accuracy of the solution the grid must be dense, meaning that the cost-to-go can require several megabytes of memory. The scope of this paper is therefore twofold. The first topic is a sensitivity study, where the effect of a sparsely gridded state is investigated, both for an 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 topic and the main contribution is a method to approximate the DP cost-to-go 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 cost-to-go. Thereby it is possible to significantly reduce the memory requirements, without any noticeable increase in simulated fuel consumption.


Viktor Larsson

Chalmers, Signals and Systems, Systems and control

Lars Johannesson

Chalmers, Signals and Systems, Systems and control

Bo Egardt

Chalmers, Signals and Systems, Systems and control

13th European Control Conference, ECC 2014; Strasbourg Convention and Exhibition CenterPlace de BordeauxStrasbourg; France; 24 June 2014 through 27 June 2014

978-395242691-3 (ISBN)

Driving Forces

Sustainable development

Areas of Advance



Subject Categories

Control Engineering





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