Time-optimal aircraft trajectories in climbing phase and singular perturbations

International audienceThis article deals with the singularly perturbed aircraft minimum time-to-climb problem. First, we introduce a reduced-order problem with affine dynamics with respect to the control and analyze it with the tools from geometric control: maximum principle combined with second order optimality conditions. Then, we compute candidates as minimizers using multiple shooting and homotopy methods for both problems, that we briefly compare numerically. Particular attention is paid to the singular extremals and we discuss about their local optimality