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Zh. Vychisl. Mat. Mat. Fiz., 2011, Volume 51, Number 4, Pages 562–579 (Mi zvmmf9225)  

This article is cited in 4 scientific papers (total in 4 papers)

Resource-optimal control of linear systems

V. M. Aleksandrov

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

Abstract: A numerical method for minimizing the resource consumption for linear dynamical systems is proposed. It is based on forming a finite-time control that steers the linear system from an arbitrary initial state to the desired terminal state in a given fixed time; this control gives an approximate solution of the problem. It is shown that the structure of the finite-time control makes it possible to determine the structure of the resource-optimal control. A method for determining an initial approximation is described, and an iterative algorithm for calculating the optimal control is proposed. A system of linear algebraic equations relating the deviations of the initial conditions in the adjoint system to the deviations of the phase coordinates from the prescribed terminal state at the terminal point in time is obtained. A computational algorithm is described. The radius of local convergence is found and the quadratic rate of convergence is established. It is proved that the computational procedure and the sequence of controls converge to the resource-optimal control.

Key words: optimal control, finite-time control, resource consumption problem, linear system, phase trajectory, switching times, adjoint system, variation, iteration, convergence of computational algorithm.

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English version:
Computational Mathematics and Mathematical Physics, 2011, 51:4, 520–536

Bibliographic databases:

UDC: 519.626.1
Received: 16.03.2009

Citation: V. M. Aleksandrov, “Resource-optimal control of linear systems”, Zh. Vychisl. Mat. Mat. Fiz., 51:4 (2011), 562–579; Comput. Math. Math. Phys., 51:4 (2011), 520–536

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. M. Aleksandrov, “A singular solution to the problem of minimizing resource consumption”, Num. Anal. Appl., 9:1 (2016), 1–11  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. V. M. Aleksandrov, “Optimal resource consumption control of perturbed systems”, Num. Anal. Appl., 10:3 (2017), 185–197  mathnet  crossref  crossref  isi  elib
    3. V. M. Aleksandrov, “Optimal resource consumption control with interval restrictions”, J. Appl. Industr. Math., 12:2 (2018), 201–212  mathnet  crossref  crossref  elib
    4. V. M. Aleksandrov, “Obschee reshenie zadachi minimizatsii raskhoda resursa”, Sib. elektron. matem. izv., 15 (2018), 1383–1409  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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