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International Conference on Numerical Computations: Theory and Algorithms

NUMTA 2019: Numerical Computations: Theory and Algorithms pp 124–138Cite as

On Polyhedral Estimates of Reachable Sets of Discrete-Time Systems with Uncertain Matrices and Integral Bounds on Additive Terms

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11974))

Abstract

We consider discrete-time systems of bilinear type for the case when interval bounds on the coefficients of the system are imposed, additive input terms are restricted by integral non-quadratic constraints, and initial states belong to given sets, which are assumed to be parallelepipeds. An approach for estimating the reachable sets is presented. It is based on considering reachable sets in the “extended” space and constructing external and internal estimates of them in the form of polytopes of some special shape. The specific cross-sections of these polytopes provide the parallelepiped-valued or parallelotope-valued estimates of the reachable sets in the “initial” space. Evolution of the estimates in the “extended” space is determined by recurrence relations. All the estimates can be calculated by explicit formulas. The main attention is paid to internal estimates. Illustrative examples are presented.

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Acknowledgments

The research was supported by the Russian Foundation for Basic Research (RFBR) under Project 18-01-00544a.

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, S.Kovalevskaja Street 16, 620108, Ekaterinburg, Russia

    Elena K. Kostousova

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  1. Elena K. Kostousova
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Correspondence to Elena K. Kostousova .

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Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

  2. University of Calabria, Rende, Italy

    Dmitri E. Kvasov

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Kostousova, E.K. (2020). On Polyhedral Estimates of Reachable Sets of Discrete-Time Systems with Uncertain Matrices and Integral Bounds on Additive Terms. In: Sergeyev, Y., Kvasov, D. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2019. Lecture Notes in Computer Science(), vol 11974. Springer, Cham. https://doi.org/10.1007/978-3-030-40616-5_10

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  • DOI: https://doi.org/10.1007/978-3-030-40616-5_10

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  • Online ISBN: 978-3-030-40616-5

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