  In this study, we propose an algorithmic framework for solving a class of
optimal control problems. This class is associated with the minimum-time
interception of moving target problems, where a plant with a given state
equation must approach a moving target whose trajectory is known a priori. Our
framework employs an analytical description of the distance from an arbitrary
point to the reachable set of the plant. The proposed algorithm is always
convergent and cannot be improved without losing the guarantee of its
convergence to the correct solution for arbitrary Lipschitz continuous
trajectories of the moving target. In practice, it is difficult to obtain an
analytical description of the distance to the reachable set for the
sophisticated state equation of the plant. Nevertheless, it was shown that the
distance can be obtained for some widely used models, such as the Dubins car,
in an explicit form. Finally, we illustrate the generality and effectiveness of
the proposed framework for simple motions and the Dubins model.
