Modelling of the space of paths in problems of constructing optimal trajectories

The basic problem of constructing optimal paths in non-simply connected domains is formulated, and the structure of its solution, based on a discrete-continual model of the space of paths, is considered. The special case of the basic problem, connected with the construction of extremals in a piecewise linear three-dimensional manifold, is studied. The proposed model is extended to problems of constructing, in non-simply-connected domain, extremals with moving end and connecting networks. The result of solving one of the problems is quoted.