Asymptotics of the optimal time in a time-optimal problem with two small parameters

A time-optimal problem of control of a small-mass point by a force of bounded magnitude in a nonresisting medium is considered. An asymptotic expansion of the optimal time and optimal control is constructed with respect to two independent small parameters: the mass of the point and the perturbation of the initial conditions. It is shown that the asymptotics of the optimal time in this problem is complicated even for cases of general position.