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Modelling and Data Analysis

Publisher: Moscow State University of Psychology and Education

ISSN (printed version): 2219-3758

ISSN (online): 2311-9454

DOI: https://doi.org/10.17759/mda

License: CC BY-NC 4.0

Started in 2011

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On a Decomposition Method in the Problem of Operation Speed for a Linear Discrete System with Bounded Control 53

Ibragimov D.N.
PhD in Physics and Matematics, Senior Lecturer, Moscow Aviation Institute (National Research University), Moscow, Russia
e-mail: rikk.dan@gmail.com

Turchak E.E.
student of magistracy, Moscow Aviation Institute (National Research University), Moscow, Russia
e-mail: turchak.kate@mail.ru

Abstract
The article presents the problem of operation speed for a linear discrete system with bounded control. For the case when the minimum number of steps necessary for the system to reach zero significantly exceeds the dimension of the phase space, a method of decomposition into scalar and two-dimensional subsystems is developed, based on the reduction of the state matrix to normal Jordan form. Moreover, due to the developed algorithm for adding two polyhedrons with linear complexity, it is possible to construct sets of 0-controllability for two-dimensional subsystems in an explicit form. A description of the main tools for solving the problem of operation speed is also presented, as well as the statement of the decomposition problem. Further, some properties of polyhedrons in the plane are formulated and proved, on the basis of which an algorithm for calculating the set of vertices of the sum of two polyhedrons in R2 in explicit form is developed. In conclusion, the main decomposition theorem is formulated and proved. And on the basis of the developed methods, the solution to the problem of the optimal damping speed of a high-rise structure located in the zone of seismic activity was constructed.

Keywords: linear discrete system, problem of operation speed, method of decomposition

Column: Short Messages

DOI: https://doi.org/10.17759/mda.2019090413

For Reference

Funding

This work was supported by the Russian Foundation for Basic Research (project № .18–08–00128-a).

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