# Geometric and numerical methods for a state constrained minimum time control problem of an electric vehicle

## TL;DR

This paper models and analyzes the minimum time control problem for an electric vehicle with state constraints, using geometric control theory and numerical methods to identify optimal solutions.

## Contribution

It introduces a geometric control approach combined with numerical techniques to solve the constrained minimum time problem for electric vehicles, advancing solution methods.

## Key findings

- Reduction of candidate solutions using geometric control techniques
- Development of numerical methods with multiple shooting and homotopy
- Successful numerical investigation with the HamPath software

## Abstract

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.