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

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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.

General Information

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

Journal rubric: Short Messages

Article type: scientific article

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

For citation: Ibragimov D.N., Turchak E.E. On a Decomposition Method in the Problem of Operation Speed for a Linear Discrete System with Bounded Control. Modelirovanie i analiz dannikh = Modelling and Data Analysis, 2019. Vol. 9, no. 4, pp. 157–161. DOI: 10.17759/mda.2019090413. (In Russ., аbstr. in Engl.)

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PhD in Physics and Matematics, Associate Professor of the Department of Probability Theory and Computer Modeling, Moscow Aviation Institute (National Research University), Moscow, Russia, ORCID: https://orcid.org/0000-0001-7472-5520, e-mail: rikk.dan@gmail.com

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

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