Abstract (EN)

Affine control problems arise naturally from controlled mechanical systems. Building on previous results [Agrachev and Biolo, J. Dyn. Control Syst., 23 (2017), pp. 577--595; Caillau and Daoud, SIAM J. Control Optim., 50 (2012), pp. 3178--3202], we prove that, in the case of time minimization with control on the disk, the extremal flow given by Pontrjagin's maximum principle is smooth along the strata of a well-chosen stratification. We also study this flow in terms of regular-singular transition and prove that the singularity along time-minimizing extremals crossing these strata is at most logarithmic. We then apply these results to mechanical systems, paying special attention to the case of the controlled three-body problem.