Geodesic
Minimizing the fuel consumption of a vehicle from the Shell Eco-marathon: a numerical study
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 2, pp. 516-532

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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.

DOI : 10.1051/cocv/2012019
Classification : 49J15, 90C90, 49N90
Keywords: optimal control, singular arcs, nonlinear programming, continuation method, indirect multiple shooting 
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     author = {Jan, Sophie},
     title = {Minimizing the fuel consumption of a vehicle from the {Shell} {Eco-marathon:} a numerical study},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {516--532},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {2},
     year = {2013},
     doi = {10.1051/cocv/2012019},
     mrnumber = {3049721},
     zbl = {1263.49034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012019/}
}
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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, Tome 19 (2013) no. 2, pp. 516-532. doi: 10.1051/cocv/2012019

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