| Issue |
ESAIM: COCV
Volume 19, Number 2, April-June 2013
|
|
|---|---|---|
| Page(s) | 516 - 532 | |
| DOI | https://doi.org/10.1051/cocv/2012019 | |
| Published online | 21 February 2013 | |
Minimizing the fuel consumption of a vehicle from the Shell Eco-marathon: a numerical study∗
Université de Toulouse & CNRS, Institut de
Mathématiques de Toulouse, UMR 5219,
31062
Toulouse Cedex 9,
France
sophie.jan@math.univ-toulouse.fr
Received: 1 June 2011
Revised: 16 January 2012
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.
Mathematics Subject Classification: 49J15 / 90C90 / 49N90
Key words: Optimal control / singular arcs / nonlinear programming / continuation method / indirect multiple shooting
© EDP Sciences, SMAI, 2013
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