  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.
