In this article, the minimum time control problem of an electric vehicle is modeled as a Mayer problem in optimal control, with affine dynamics with respect to the control and with state constraints. The candidates as minimizers are selected among a set of extremals, solutions of a Hamiltonian system given by the maximum principle. An analysis, with the techniques of geometric control, is used first to reduce the set of candidates and then to construct the numerical methods. This leads to a numerical investigation based on indirect methods using the HamPath software. Multiple shooting and homotopy techniques are used to build a synthesis with respect to the bounds of the boundary sets.

Accepted:

DOI: 10.1051/cocv/2016070

Keywords: Geometric optimal control, state constraints, shooting and homotopy methods, electric car

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@article{COCV_2017__23_4_1715_0, author = {Cots, Olivier}, title = {Geometric and numerical methods for a state constrained minimum time control problem of an electric vehicle}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1715--1749}, publisher = {EDP-Sciences}, volume = {23}, number = {4}, year = {2017}, doi = {10.1051/cocv/2016070}, mrnumber = {3716938}, zbl = {1379.49025}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2016070/} }

TY - JOUR AU - Cots, Olivier TI - Geometric and numerical methods for a state constrained minimum time control problem of an electric vehicle JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 1715 EP - 1749 VL - 23 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2016070/ DO - 10.1051/cocv/2016070 LA - en ID - COCV_2017__23_4_1715_0 ER -

%0 Journal Article %A Cots, Olivier %T Geometric and numerical methods for a state constrained minimum time control problem of an electric vehicle %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 1715-1749 %V 23 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2016070/ %R 10.1051/cocv/2016070 %G en %F COCV_2017__23_4_1715_0

Cots, Olivier. Geometric and numerical methods for a state constrained minimum time control problem of an electric vehicle. ESAIM: Control, Optimisation and Calculus of Variations, Volume 23 (2017) no. 4, pp. 1715-1749. doi : 10.1051/cocv/2016070. http://archive.numdam.org/articles/10.1051/cocv/2016070/

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