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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 5, Pages 758–775 (Mi zvmmf10200)  
This article is cited in 3 scientific papers (total in 3 papers)

Optimal control of linear systems with interval constraints

V. M. Aleksandrov

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090, Russia

Abstract: For linear systems with interval constraints, a method for computing a time-optimal control is proposed. The method is based on transforming a quasi-optimal control. The properties and features of the quasi-optimal control are examined. A technique is described for dividing the domain of initial conditions into reachable sets over different times and for approximating each set by a family of hyperplanes. An iterative method for computing an optimal control with interval constraints is developed. The convergence of the method is proved, and a sufficient condition for the convergence of the computational process is obtained. The radius of local quadratic convergence is found. Numerical results are presented.

Key words: optimal control, quasi-optimal control, interval constraints, time-optimal control, reachable set, adjoint system, convergence, iterative process.

DOI: https://doi.org/10.7868/S004446691505004X

Full text: PDF file (302 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:5, 749–765

Bibliographic databases:

UDC: 519.626
MSC: Primary 49M20; Secondary 49M05
Received: 07.08.2014
Revised: 16.11.2014

Citation: V. M. Aleksandrov, “Optimal control of linear systems with interval constraints”, Zh. Vychisl. Mat. Mat. Fiz., 55:5 (2015), 758–775; Comput. Math. Math. Phys., 55:5 (2015), 749–765

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. B. Rudnitskii, N. N. Dikhtyaruk, “Interaction between an infinite stringer and two identical prestressed strips: contact problem”, Int. Appl. Mech., 53:2 (2017), 149–155  crossref  mathscinet  isi
    2. V. M. Aleksandrov, “Optimal resource consumption control with interval restrictions”, J. Appl. Industr. Math., 12:2 (2018), 201–212  mathnet  crossref  crossref  elib
    3. Dikhtyaruk N.N., Kurinenko O.V., Poplavskaya E.A., Samaruk N.N., “Interaction Between a Finite Stringer and Two Identical Prestressed Strips: Contact Problem”, Int. Appl. Mech., 55:1 (2019), 79–85  crossref  mathscinet  isi  scopus
    		• Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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