Navigation and routes planning for a group of unmanned surface vessels (USV) jointly moving in complex environment, including circumvention of seashore and islands, are important applications of computer-based decision-making support systems. A group of objects as an open complex system includes several hierarchy levels and may be controlled by a decision-maker supported by information-analytical software and methodical maintenance. Planning, as a stage of management, includes an a priori phase guidance for all objects in the group, coordinated in both time and directions of approach to the target set restricted by a set of obstacles. A discrete system of priorities reflects relative preferences of importance and allows choosing routes optimal in different senses. One can formalize such tasks in terms of different mathematical models including control problems of formation motion, theory of extreme networks and interval analysis. The paper bases on guaranteed approach to control of dynamic objects under uncertainty. Unified mathematical descriptions of shores, routes of individual objects and the whole group may be given in terms of hierarchic (i)-systems. This allows to reconcile data on geography, environment, object characteristics, peculiarities of control systems and data transmission, including sources and causes of uncertainty, and to describe movement of a group as an extreme problem of control and estimation. The results of computer simulation are considered. One may use similar models to explore economic aspects in application of heterogenic complex of autonomous surface and underwater vessels.
Application of a Volterra quadratic polynomial to modeling elements of heat engineering devices
