Minimizing the fuel consumption of a vehicle from the Shell Eco-marathon: a numerical study

Sophie Jan

ESAIM: Control, Optimisation and Calculus of Variations (2013)

  • Volume: 19, Issue: 2, page 516-532
  • ISSN: 1292-8119

Abstract

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We apply four different methods to study an intrinsically bang-bang optimal control problem. We study first a relaxed problem that we solve with a naive nonlinear programming approach. Since these preliminary results reveal singular arcs, we then use Pontryagin’s Minimum Principle and apply multiple indirect shooting methods combined with homotopy approach to obtain an accurate solution of the relaxed problem. Finally, in order to recover a purely bang-bang solution for the original problem, we use once again a nonlinear programming approach.

How to cite

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Jan, Sophie. "Minimizing the fuel consumption of a vehicle from the Shell Eco-marathon: a numerical study." ESAIM: Control, Optimisation and Calculus of Variations 19.2 (2013): 516-532. <http://eudml.org/doc/272889>.

@article{Jan2013,
abstract = {We apply four different methods to study an intrinsically bang-bang optimal control problem. We study first a relaxed problem that we solve with a naive nonlinear programming approach. Since these preliminary results reveal singular arcs, we then use Pontryagin’s Minimum Principle and apply multiple indirect shooting methods combined with homotopy approach to obtain an accurate solution of the relaxed problem. Finally, in order to recover a purely bang-bang solution for the original problem, we use once again a nonlinear programming approach.},
author = {Jan, Sophie},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {optimal control; singular arcs; nonlinear programming; continuation method; indirect multiple shooting; bang-bang solution},
language = {eng},
number = {2},
pages = {516-532},
publisher = {EDP-Sciences},
title = {Minimizing the fuel consumption of a vehicle from the Shell Eco-marathon: a numerical study},
url = {http://eudml.org/doc/272889},
volume = {19},
year = {2013},
}

TY - JOUR
AU - Jan, Sophie
TI - Minimizing the fuel consumption of a vehicle from the Shell Eco-marathon: a numerical study
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2013
PB - EDP-Sciences
VL - 19
IS - 2
SP - 516
EP - 532
AB - We apply four different methods to study an intrinsically bang-bang optimal control problem. We study first a relaxed problem that we solve with a naive nonlinear programming approach. Since these preliminary results reveal singular arcs, we then use Pontryagin’s Minimum Principle and apply multiple indirect shooting methods combined with homotopy approach to obtain an accurate solution of the relaxed problem. Finally, in order to recover a purely bang-bang solution for the original problem, we use once again a nonlinear programming approach.
LA - eng
KW - optimal control; singular arcs; nonlinear programming; continuation method; indirect multiple shooting; bang-bang solution
UR - http://eudml.org/doc/272889
ER -

References

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  8. [8] H.M. Robbins, A generalized Legendre-Clebsch condition for the singular cases of optimal control. IBM J. Research Devel.11 (1967) 361–372. Zbl0153.41202
  9. [9] S. Sager, H. G. Bock, M. Diehl, G. Reinelt and J. P. Schlöder, Numerical methods for optimal control with binary control functions applied to a Lotka-Volterra type fishing problem, in Recent advances in optimization, Lect. Notes Econ. Math. Syst. 563 (2006) 269–289. Zbl1107.49023MR2191163
  10. [10] J. Stoer and R. Bulirsch, Introduction to numerical analysis. Translated from the German by R. Bartels, W. Gautschi and C. Witzgall, Springer-Verlag (1980). Zbl0423.65002MR557543
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