CONSTRUCTION OF RESOLVING STRUCTURES IN A CLASS OF SPATIAL TIME-OPTIMAL PROBLEMS: THE CASE OF A NON-CONVEX TARGET SET WITH NEGATIVE GAUSSIAN CURVATURE OF ITS BOUNDARY

The problem of high-speed response in three-dimensional space with a spherical velocity vectorgram and a non-convex target set is studied. A feature of the solution of the problem is the presence of a scattering surface (bisector), from the points of which at least two optimal trajectories emanate. Formulas for the extreme points of the bisector are derived for the case when the boundary of the target set is a surface of negative Gaussian curvature. The relative positions of points on the target set, to which optimal trajectories come from the scattering surface, are studied. An example of solving the high-speed problem is given in the form of a set of level surfaces of the optimal result function with the selection of a set of points at which the smoothness of these surfaces is violated.