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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2007, Volume 10, Number 1, Pages 1–28 (Mi sjvm64)  

This article is cited in 14 scientific papers (total in 14 papers)

Iterative method for computing time optimal control in real time mode

V. M. Aleksandrov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
References:
Abstract: We propose a simple method for forming a piecewise constant finite control in the real-time mode, which transfers a linear system from any initial state to the origin in a fixed time. The relations for a sequence of finite controls to be transformed into the fast time optimal control are obtained. Computations are carried out while the system is monitored. The iterative process of computing the optimal control reduces to a sequence of solutions to linear algebraic equations and the Cauchy problems. Effective techniques for setting an initial approximation are proposed, which significantly decrease the number of iterations. A sequence of finite controls is proved to converge to the time optimal control. Results of modeling and computing are given.
Key words: optimal control, finite control, linear system, phase trajectory, speed, switching moments, adjoint system, variation, iteration.
Received: 01.11.2005
Revised: 17.03.2006
UDC: 517.977.58
Language: Russian
Citation: V. M. Aleksandrov, “Iterative method for computing time optimal control in real time mode”, Sib. Zh. Vychisl. Mat., 10:1 (2007), 1–28
Citation in format AMSBIB
\Bibitem{Ale07}
\by V.~M.~Aleksandrov
\paper Iterative method for computing time optimal control in real time mode
\jour Sib. Zh. Vychisl. Mat.
\yr 2007
\vol 10
\issue 1
\pages 1--28
\mathnet{http://mi.mathnet.ru/sjvm64}
Linking options:
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  • https://www.mathnet.ru/eng/sjvm/v10/i1/p1
  • This publication is cited in the following 14 articles:
    1. V. M. Aleksandrov, “Optimal resource consumption control with interval restrictions”, J. Appl. Industr. Math., 12:2 (2018), 201–212  mathnet  crossref  crossref  elib
    2. V. M. Aleksandrov, “Obschee reshenie zadachi minimizatsii raskhoda resursa”, Sib. elektron. matem. izv., 15 (2018), 1383–1409  mathnet  crossref
    3. V. M. Aleksandrov, “Optimal resource consumption control of perturbed systems”, Num. Anal. Appl., 10:3 (2017), 185–197  mathnet  crossref  crossref  isi  elib
    4. 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
    5. A. V. Chernov, “O gladkosti approksimirovannoi zadachi optimizatsii sistemy Gursa–Darbu na variruemoi oblasti”, Tr. IMM UrO RAN, 20, no. 1, 2014, 305–321  mathnet  mathscinet  elib
    6. I. B. Abbasov, “Three-dimensional simulation of the runup of nonlinear surface gravity waves”, Comput. Math. Math. Phys., 54:5 (2014), 871–886  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. V. M. Aleksandrov, “Transferring a system with unknown disturbance under optimal control to a state of dynamic balance and to ϵϵ-vicinity of a final state”, Num. Anal. Appl., 6:2 (2013), 119–130  mathnet  crossref  mathscinet  elib
    8. V. M. Aleksandrov, “Optimalnoe upravlenie dinamicheskoi sistemoi pri nepolnoi informatsii”, Sib. elektron. matem. izv., 9 (2012), 329–345  mathnet
    9. V. M. Aleksandrov, “Real-time computation of optimal control”, Comput. Math. Math. Phys., 52:10 (2012), 1351–1372  mathnet  crossref  mathscinet  zmath
    10. Chernov A.V., “O priblizhennom reshenii zadach optimalnogo upravleniya so svobodnym vremenem”, Vestnik nizhegorodskogo universiteta im. N.I. Lobachevskogo, 2012, 107–114 On approximate solution of free time optimal control problems  elib
    11. V. M. Aleksandrov, “Features of motion of dynamic systems with disturbances in the neighborhood of manifolds of switchings”, Autom. Remote Control, 70:4 (2009), 615–632  mathnet  crossref  mathscinet  zmath  isi
    12. V. M. Aleksandrov, “Optimalnoe po bystrodeistviyu pozitsionno-programmnoe upravlenie lineinymi dinamicheskimi sistemami”, Sib. elektron. matem. izv., 6 (2009), 385–439  mathnet  mathscinet
    13. Zuliang Lu, Yanping Chen, “LL-error estimates of triangular mixed finite element methods for optimal control problems governed by semilinear elliptic equations”, Num. Anal. Appl., 2:1 (2009), 74–86  mathnet  crossref
    14. V. M. Aleksandrov, “Optimalnoe po bystrodeistviyu upravlenie v realnom vremeni lineinymi sistemami s vozmuscheniyami”, Vestn. NGU. Ser. matem., mekh., inform., 8:3 (2008), 3–25  mathnet
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