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

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

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
\Bibitem{Ale11} \by V.~M.~Aleksandrov \paper Resource-optimal control of linear systems \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2011 \vol 51 \issue 4 \pages 562--579 \mathnet{http://mi.mathnet.ru/zvmmf9225} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2858619} \transl \jour Comput. Math. Math. Phys. \yr 2011 \vol 51 \issue 4 \pages 520--536 \crossref{https://doi.org/10.1134/S0965542511040014} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000290035800003} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79955595116} 

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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
2. V. M. Aleksandrov, “Optimal resource consumption control of perturbed systems”, Num. Anal. Appl., 10:3 (2017), 185–197
3. V. M. Aleksandrov, “Optimal resource consumption control with interval restrictions”, J. Appl. Industr. Math., 12:2 (2018), 201–212
4. V. M. Aleksandrov, “Obschee reshenie zadachi minimizatsii raskhoda resursa”, Sib. elektron. matem. izv., 15 (2018), 1383–1409
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