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

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

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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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. 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
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
3. Maksimov V.I., “Differential Guidance Game With Incomplete Information on the State Coordinates and Unknown Initial State”, Differ. Equ., 51:12 (2015), 1656–1665
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
5. V. I. Maksimov, “On a guaranteed guidance problem under incomplete information”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 147–158
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
7. Maksimov V.I., “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
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
9. Maksimov V.I., “Problem of Guaranteed Guidance By Measuring Part of the State Vector Coordinates”, Differ. Equ., 53:11 (2017), 1449–1457
10. Surkov Platon Gennad'evich, “the Problem of Package Guidance Under Incomplete Information and Integral Signal of Observation”, Sib. Electron. Math. Rep., 15 (2018), 373–388
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