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Avtomatika i Telemekhanika, 2021, Issue 12, Pages 48–72
DOI: https://doi.org/10.31857/S0005231021120047 (Mi at15852) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Linear Systems

On sufficient optimality conditions for a guaranteed control in the speed problem for a linear time-varying discrete-time system with bounded control

D. N. Ibragimov, N. M. Novozhilkin, E. Yu. Porceva

Moscow Aviation Institute, Moscow, 125993 Russia
Full-text PDF (592 kB) Citations (12)
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DOI: https://doi.org/10.31857/S0005231021120047
Abstract: We consider the solution of the speed problem for linear time-varying discrete-time systems with convex control constraints. A method is proposed for reducing the general case of the speed problem to the case of linear control constraints using polyhedral approximation algorithms. Sufficient optimality conditions for the guaranteed solution are stated and proved. Examples are given. Based on the methods obtained, the speed-optimal damping problem for a high-rise structure located in a seismic activity zone is solved.
Keywords: discrete-time control system, speed problem, optimal positional control, linear programming problem, controllability set, convex polyhedron, polyhedral approximation.
Funding agency Grant number
Russian Foundation for Basic Research 18-08-00128_а
This work was financially supported by the Russian Foundation for Basic Research, project no. 18-08-00128-a.
Presented by the member of Editorial Board: A. I. Kibzun

Received: 21.06.2020
Revised: 03.06.2021
Accepted: 30.06.2021
English version:
Automation and Remote Control, 2021, Volume 82, Issue 12, Pages 2076–2096
DOI: https://doi.org/10.1134/S000511792112002X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: D. N. Ibragimov, N. M. Novozhilkin, E. Yu. Porceva, “On sufficient optimality conditions for a guaranteed control in the speed problem for a linear time-varying discrete-time system with bounded control”, Avtomat. i Telemekh., 2021, no. 12, 48–72; Autom. Remote Control, 82:12 (2021), 2076–2096
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/at15852
  • https://www.mathnet.ru/eng/at/y2021/i12/p48
    • This publication is cited in the following 12 articles:
    1. S.R. Guseva, D.N. Ibragimov, “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 (2025), 110  crossref
    2. D.N. Ibragimov, S.S. Samonov, “On the conditions of limited sets of reachability and controllability for linear systems with discrete time and total first-order constraints on scalar control”, Modelling and Data Analysis, 15:1 (2025), 51  crossref
    3. V.M. Podgornaya, “On the Suboptimal Solution of the Speed-In-Action Problem for a Linear Discrete System in the Case of Asymmetric Control Constraints”, Modelling and Data Analysis, 14:3 (2024), 63  crossref
    4. D. N Ibragimov, K. A Tsarkov, “On an Approach to Solving the Time-Optimization Problem for Linear Discrete-Time Systems Based on Krotov Method”, Avtomatika i telemehanika, 2024, no. 11, 3  crossref
    5. Danis N. Ibragimov, Communications in Computer and Information Science, 2239, Mathematical Optimization Theory and Operations Research: Recent Trends, 2024, 199  crossref
    6. D. N. Ibragimov, K. A. Tsarkov, “On an Approach to Solving the Time-Optimization Problem for Linear Discrete-Time Systems Based on Krotov Method”, Autom Remote Control, 85:11 (2024), 939  crossref
    7. D. N. Ibragimov, V. M. Podgornaya, “Construction of the time-optimal bounded control for linear discrete-time systems based on the method of superellipsoidal approximation”, Autom. Remote Control, 84:9 (2023), 1041–1064  mathnet  crossref  crossref
    8. D. N. Ibragimov, V. M. Podgornaya, “Construction of the Time-Optimal Bounded Control for Linear Discrete-Time Systems Based on the Method of Superellipsoidal Approximation”, Autom Remote Control, 84:9 (2023), 924  crossref
    9. Sümeyye Ar Güneş, Mehmet Emir Köksal, “Decomposition of Second-Order Discrete-Time Linear Time-Varying Systems into First-Order Commutative Pairs”, Circuits Syst Signal Process, 42:5 (2023), 2723  crossref
    10. Danis N. Ibragimov, Sofya R. Guseva, Lecture Notes in Computer Science, 13930, Mathematical Optimization Theory and Operations Research, 2023, 378  crossref
    11. A.A. Mokhnacheva, K.V. Gerasimova, D.N. Ibragimov, “Methods of Numerical Simulation of 0-Controllable Sets of a Linear Discrete Dynamical System with Limited Control Based on Polyhedral Approximation Algorithms”, Modelling and Data Analysis, 13:4 (2023), 84  crossref
    12. D.N. Ibragimov, V.M. Podgornaya, “Superellipsoidal Approximations in the Speed-in-action Problem for a Two-dimensional Linear Discrete System with Bounded Control”, Modelling and Data Analysis, 13:2 (2023), 151  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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