New Approaches to Modelling Covering Problems in Monitoring Optimization

An issue of mathematical modeling in design of monitoring, diagnostic, and control systems is investigated. Mathematical models of the design problems reducible to covering of a circle object by circles are built. They are based on extracting a combinatorial structure of a new type connected with multipermutatons, on exploiting new geometric properties of objects involved, as well as on applying a continuous functional representation theory for modeling of the multipermutation set. Also, a Method of Artifical Space Dilation was used for constructing one of the mathematical models in extended space. This model is a global optimization one, which is the most promising in terms of obtaining a local optimum close to a global one. The models presented are generalized directly onto problems of covering a circular object by smaller circular objects that allows to cover a much wider class of the design problems regarding their mathematical modeling and solving by continuous and discrete optimization methods.