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Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 3, Pages 132–147 (Mi timm1090)  

This article is cited in 9 scientific papers (total in 9 papers)

An open-loop criterion for the solvability of a closed-loop guidance problem with incomplete information. Linear control systems

A. V. Kryazhimskiyab, N. V. Strelkovskiycb

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b International Institute for Applied Systems Analysis, Laxenburg, Astria
c Lomonosov Moscow State University

Abstract: The method of open-loop control packages is a tool for stating the solvability of guaranteed closed-loop control problems under incomplete information on the observed states. In this paper, the method is specified for the problem of guaranteed closed-loop guidance of a linear control system to a convex target set at a prescribed point in time. It is assumed that the observed signal on the system's states is linear and the set of its admissible initial states is finite. It is proved that the problem under consideration is equivalent to the problem of open-loop guidance of an extended linear control system to an extended convex target set. Using a separation theorem for convex sets, a solvability criterion is derived, which reduces to a solution of a finite-dimensional optimization problem. An illustrative example is considered.

Keywords: control, incomplete information, linear systems.

Funding Agency Grant Number
Russian Science Foundation 14-11-00539


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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, 291, suppl. 1, 113–127

Bibliographic databases:

Document Type: Article
UDC: 517.977
Received: 03.05.2014

Citation: A. V. Kryazhimskiy, N. V. Strelkovskiy, “An open-loop criterion for the solvability of a closed-loop guidance problem with incomplete information. Linear control systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 3, 2014, 132–147; Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 113–127

Citation in format AMSBIB
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\paper An open-loop criterion for the solvability of a~closed-loop guidance problem with incomplete information. Linear control systems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2014
\vol 20
\issue 3
\pages 132--147
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\pages 113--127
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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. A. V. Kryazhimskii, N. V. Strelkovskii, “Zadacha garantirovannogo pozitsionnogo navedeniya lineinoi upravlyaemoi sistemy k zadannomu momentu vremeni pri nepolnoi informatsii. Programmnyi kriterii razreshimosti”, Tr. IMM UrO RAN, 20, no. 4, 2014, 168–177  mathnet  mathscinet  elib
    2. V. L. Rozenberg, “A control problem under incomplete information for a linear stochastic differential equation”, Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 145–155  mathnet  crossref  mathscinet  elib
    3. V. I. Maksimov, “Differential guidance game with incomplete information on the state coordinates and unknown initial state”, Differ. Equ., 51:12 (2015), 1656–1665  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    4. M. S. Blizorukova, “On a control problem for a linear system with delay in the control”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 35–42  mathnet  crossref  crossref  mathscinet  isi  elib
    5. V. I. Maksimov, “On a guaranteed guidance problem under incomplete information”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 147–158  mathnet  crossref  crossref  mathscinet  isi  elib
    6. P. G. Surkov, “The problem of closed-loop guidance by a given time for a linear control system with delay”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 218–227  mathnet  crossref  crossref  mathscinet  isi  elib
    7. V. I. Maksimov, “Guidance problem for a distributed system with incomplete information on the state coordinates and an unknown initial state”, Differ. Equ., 52:11 (2016), 1442–1452  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    8. V. I. Maksimov, P. G. Surkov, “O razreshimosti zadachi garantirovannogo paketnogo navedeniya na sistemu tselevykh mnozhestv”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:3 (2017), 344–354  mathnet  crossref  elib
    9. P. G. Surkov, “Zadacha paketnogo navedeniya s nepolnoi informatsiei pri integralnom signale nablyudeniya”, Sib. elektron. matem. izv., 15 (2018), 373–388  mathnet  crossref  mathscinet  zmath  isi
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