Abstract
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.
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