Generolo Jono Žemaičio Lietuvos karo akademija

This paper investigates the problem of constructing predicted estimates for dynamic systems described by difference equations under uncertainty. In particular, the Richardson Arms Model is considered for two competing countries, which can be used to describe the dynamics of their armaments. The main attention is paid to the case when the armament level of one of the countries under consideration is partially unknown. The function describing this level belongs to given compact and convex sets, while the values of the system variables are known only at certain discrete moments of time. An approach is proposed to find the optimal strategy of the first country, which guarantees the achievement of a given result with the maximum uncertainty value with respect to the second country. Analytical relations for determining the maximum values of uncertain quantities are obtained and substantiated. The developed approach is based on the use of properties of convex sets, vector representations, and methods of analysis of dynamic systems. A number of statements and their consequences are proved, which ensure the efficient calculation of estimates in the presence of additional restrictions on the system parameters. The proposed approach can be applied to modeling and analyzing processes of population dynamics, information dissemination, and other socio-economic systems in conditions of incomplete information regarding the state of the system.

In this article, we investigate the problem of estimating the spectral characteristics of the intensity of moving objects under stochastic uncertainty based on the results of measuring the magnitudes of wave fields at separate points. We assume that the unknown spectral functions belong to known sets from the functional space, and certain restrictions are given for the unknown correlation matrices. For linear guaranteed estimates of the set of linear functionals from spectral functions, we prove that the guaranteed mean square estimates are expressed in terms of solutions of a certain system of linear algebraic equations.