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**Harvard**

Larsson, V., Johannesson, L. och Egardt, B. (2014) *Cubic Spline Approximations of the Dynamic Programming Cost-to-go in HEV Energy Management Problems*.

** BibTeX **

@conference{

Larsson2014,

author={Larsson, Viktor and Johannesson, Lars and Egardt, Bo},

title={Cubic Spline Approximations of the Dynamic Programming Cost-to-go in HEV Energy Management Problems},

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

isbn={978-395242691-3},

pages={1699-1704},

abstract={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.},

year={2014},

}

** RefWorks **

RT Conference Proceedings

SR Electronic

ID 198988

A1 Larsson, Viktor

A1 Johannesson, Lars

A1 Egardt, Bo

T1 Cubic Spline Approximations of the Dynamic Programming Cost-to-go in HEV Energy Management Problems

YR 2014

T2 13th European Control Conference, ECC 2014; Strasbourg Convention and Exhibition CenterPlace de BordeauxStrasbourg; France; 24 June 2014 through 27 June 2014

SN 978-395242691-3

SP 1699

OP 1704

AB 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.

LA eng

DO 10.1109/ECC.2014.6862404

LK http://dx.doi.org/10.1109/ECC.2014.6862404

OL 30