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Modelling and Data Analysis
2025. Vol. 15, no. 1, 110–132
doi:10.17759/mda.2025150106
ISSN: 2219-3758 / 2311-9454 (online)

A priori estimation of the minimal stabilization time for linear discrete-time systems with bounded control based on the apparatus of eigensets

 
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Abstract

A linear system with discrete time and bounded control is considered. It is assumed that the system matrix is non-singular and diagonalizable, and the set of admissible control values is convex and compact. For a given system, the time-optimization problem is studied. In particular, it is required to construct a priori estimates of the optimal value of the minimal time as a function of the initial state and system parameters that do not require an exact construction of the class of null-controllable sets. To solve the problem, an apparatus of eigensets of a linear transformation is developed, and basic properties of non-trivial eigensets are formulated and proven. For the simplest case, when the set of admissible control values is a non-trivial eigenset of the system matrix, the response time function for a given initial state is constructed explicitly. For an arbitrary control system, a method is proposed for reducing to the simplest case by constructing internal and external approximations of a set of constraints on control values. Numerical calculations are presented demonstrating the efficiency and accuracy of the developed technique.

General Information

Keywords: linear system, discrete time, time-optimization problem, optimal control, a priori estimates of the optimal value of the objective function, eigenset

Journal rubric: Optimization Methods

Article type: scientific article

DOI: https://doi.org/10.17759/mda.2025150106

Received 13.01.2025

Published

For citation: Guseva, S.R., Ibragimov, D.N. (2025). A priori estimation of the minimal stabilization time for linear discrete-time systems with bounded control based on the apparatus of eigensets. Modelling and Data Analysis, 15(1), 110–132. (In Russ.). https://doi.org/10.17759/mda.2025150106

© Guseva S.R., Ibragimov D.N., 2025

License: CC BY-NC 4.0

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Information About the Authors

Sofya R. Guseva, Student, Department of Probability Theory and Computer Modeling, Moscow Aviation Institute (National Research University) (MAI), Moscow, Russian Federation, ORCID: https://orcid.org/0000-0002-4625-7798, e-mail: son1522@yandex.ru

Danis N. Ibragimov, Candidate of Science (Physics and Matematics), Associate Professor of Educational Center of Institute No. 8 Computer Science and Applied Mathematics, Moscow Aviation Institute (national research university) (MAI), Moscow, Russian Federation, ORCID: https://orcid.org/0000-0001-7472-5520, e-mail: rikk.dan@gmail.com

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