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Uspekhi Mat. Nauk, 2006, Volume 61, Issue 4(370), Pages 25–76 (Mi umn1760)  

This article is cited in 36 scientific papers (total in 36 papers)

Control packages: an approach to solution of positional control problems with incomplete information

Yu. S. Osipov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: An approach is proposed for solving problems of positional control of a dynamical system under conditions of incomplete information about its current phase states. The basis of this approach is a new notion of control packages, namely, procedures for constructing control programs which are non-anticipatory with respect to the dynamics of observations. For definiteness, the approach is realised for a concrete control problem of guaranteed guidance of a controlled system to a given target set at a fixed moment of time. The main result of the paper states that the indicated problem is soluble in the class of positional strategies if and only if it is soluble in the class of control packages. This result shows a way to reduce control problems in the positional (closed-loop) formulation to control problems in the program (open-loop) formulation. In this sense a methodology for program constructions is developed that is well known in the theory of positional differential games.

DOI: https://doi.org/10.4213/rm1760

Full text: PDF file (827 kB)
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English version:
Russian Mathematical Surveys, 2006, 61:4, 611–661

Bibliographic databases:

UDC: 517.977.5
MSC: Primary 91A24, 93C41; Secondary 49N75
Received: 04.05.2006

Citation: Yu. S. Osipov, “Control packages: an approach to solution of positional control problems with incomplete information”, Uspekhi Mat. Nauk, 61:4(370) (2006), 25–76; Russian Math. Surveys, 61:4 (2006), 611–661

Citation in format AMSBIB
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    This publication is cited in the following articles:
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    4. A. V. Kryazhimskiy, Yu. S. Osipov, “Idealized program packages and problems of positional control with incomplete information”, Proc. Steklov Inst. Math. (Suppl.), 268, suppl. 1 (2010), S155–S174  mathnet  crossref  isi  elib
    5. V. I. Maksimov, “Tracking a reference solution of a control system of phase field equations”, Proc. Steklov Inst. Math., 271 (2010), 138–148  mathnet  crossref  mathscinet  isi  elib
    6. A. V. Kryazhimskii, “Numerical encoding of sampled controls and an approximation metric criterion for the solvability of an aiming game problem”, Proc. Steklov Inst. Math. (Suppl.), 276, suppl. 1 (2012), S106–S125  mathnet  crossref  zmath  isi  elib  elib
    7. S. N. Vassilyev, G. M. Ponomarev, “Automation methods for logical derivation and their application in the control of dynamic and intelligent systems”, Proc. Steklov Inst. Math. (Suppl.), 276, suppl. 1 (2012), S161–S179  mathnet  crossref  isi  elib
    8. A. V. Kryazhimskiy, Yu. S. Osipov, “On the solvability of problems of guaranteeing control for partially observable linear dynamical systems”, Proc. Steklov Inst. Math., 277 (2012), 144–159  mathnet  crossref  mathscinet  isi  elib  elib
    9. V. M. Aleksandrov, “Real-time computation of optimal control”, Comput. Math. Math. Phys., 52:10 (2012), 1351–1372  mathnet  crossref  mathscinet  zmath
    10. V. I. Maksimov, “On designing a reconstruction-control algorithm for an ecological-economic model”, Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 102–115  mathnet  crossref  mathscinet  isi  elib
    11. V. M. Aleksandrov, “Zadanie nachalnogo priblizheniya i metod vychisleniya optimalnogo upravleniya”, Sib. elektron. matem. izv., 11 (2014), 87–118  mathnet
    12. 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”, Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 113–127  mathnet  crossref  mathscinet  isi  elib
    13. 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
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    15. N. V. Strelkovskii, “Constructing a strategy for the guaranteed positioning guidance of a linear controlled system with incomplete data”, MoscowUniv.Comput.Math.Cybern, 39:3 (2015), 126  crossref  mathscinet  zmath
    16. 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
    17. N. L. Grigorenko, A. E. Rumyantsev, “On a class of control problems with incomplete information”, Proc. Steklov Inst. Math., 291 (2015), 68–77  mathnet  crossref  crossref  isi  elib
    18. V. S. Kublanov, V. I. Maksimov, “On feedback-principle control for systems with aftereffect under incomplete phase-coordinate data”, Journal of Mathematical Sciences, 233:4 (2018), 495–513  mathnet  crossref
    19. Maksimov V.I., “Differential Guidance Game With Incomplete Information on the State Coordinates and Unknown Initial State”, Diff. Eq., 51:12 (2015), 1656–1665  crossref  mathscinet  zmath  isi
    20. Valeriy L. Rozenberg, “A guaranteed control problem for a linear stochastic differential equation”, Ural Math. J., 1:1 (2015), 68–82  mathnet  crossref
    21. 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
    22. 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
    23. N. L. Grigorenko, A. E. Rumyantsev, “Terminal control of a nonlinear process under disturbances”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 108–116  mathnet  crossref  crossref  mathscinet  isi  elib
    24. A. A. Dryazhenkov, M. M. Potapov, “Numerical solution of the positional boundary control problem for the wave equation with unknown initial data”, Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 22–30  mathnet  crossref  crossref  mathscinet  isi  elib
    25. 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
    26. 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
    27. V. I. Maksimov, “On a problem of linear system control under incomplete information about the phase coordinates”, Autom. Remote Control, 77:6 (2016), 943–958  mathnet  crossref  isi  elib  elib
    28. V. M. Aleksandrov, “Quasi-optimal control of dynamic systems”, Autom. Remote Control, 77:7 (2016), 1163–1179  mathnet  crossref  isi  elib  elib
    29. 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  crossref  mathscinet  zmath  isi  scopus
    30. V. M. Aleksandrov, “Optimal resource consumption control of perturbed systems”, Num. Anal. Appl., 10:3 (2017), 185–197  mathnet  crossref  crossref  isi  elib
    31. 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
    32. Maksimov V.I., “Problem of Guaranteed Guidance By Measuring Part of the State Vector Coordinates”, Differ. Equ., 53:11 (2017), 1449–1457  crossref  mathscinet  zmath  isi  scopus
    33. 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
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