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REACHABLE SET OF SOME DISCRETE SYSTEM WITH UNCERTAIN LIU DISTURBANCES | Ananyev | Ural Mathematical Journal

REACHABLE SET OF SOME DISCRETE SYSTEM WITH UNCERTAIN LIU DISTURBANCES

Boris I. Ananyev     (Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620108, Russian Federation)

Abstract


In this paper, we consider a problem of finding of the attainability set for a linear system with determinate and stochastic Liu's uncertainties. In the capacity of Liu's disturbances are used ordinary uniformly distributed and independent among themselves uncertain values defined on some uncertain space. This fact means that the state vector of the system and the entire problem become infinite dimensional one. As the determinate disturbances are taken in attention feedback controls and unknown initial states. Besides, the restriction in the form of the sum of uncertain expectations is set. The initial estimation problem is reduced to the determinate multistage problem for matrices and with the fixed restriction on the right end of trajectory. This reduction demands some information about Liu's theory. We give necessary and sufficient conditions for finiteness of target functional in the obtained determinate problem. A numerical example for two-dimensional and two-stage system is given.

Keywords


uncertainty theory, uncertain values, feedback controls, attainable set, Lagrange multipliers

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References


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DOI: http://dx.doi.org/10.15826/umj.2024.2.002
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