We consider the construction of an adaptive algorithm for solving a boundary value problem ensuring that a trajectory issuing from some point hits a finite-size target at a given time under partial uncertainty in the disturbance field. Although the disturbance field has a component that is unknown in explicit form but is still important for hitting a target of given size, we have constructed an iteration procedure for solving the problem in finitely many steps under a number of conditions. The algorithm is based on trial trajectories and uses the measurement of their deviations from the target center as a feedback; this proves sufficient to compensate for the incompleteness of information about the external disturbance field.