On Singularities of Minimum Time Control-Affine Systems

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 Daoud, SIAM Optim., 50 (2012), 3178--3202], we prove that, in the case of time minimization with disk, extremal flow given by Pontrjagin's maximum principle is smooth along strata a well-chosen stratification. We also study this terms regular-singular transition that singularity time-minimizing extremals crossing these at most logarithmic. then apply to systems, paying special attention three-body problem.