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.
Citation:
Yu. S. Osipov, “Control packages: an approach to solution of positional control problems with incomplete information”, Russian Math. Surveys, 61:4 (2006), 611–661
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\by Yu.~S.~Osipov
\paper Control packages: an approach to solution of positional control problems with incomplete information
\jour Russian Math. Surveys
\yr 2006
\vol 61
\issue 4
\pages 611--661
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Linking options:
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This publication is cited in the following 48 articles:
P. G. Surkov, “Package guidance problem for a fractional-order system”, Proc. Steklov Inst. Math. (Suppl.), 325, suppl. 1 (2024), S212–S230
Osipov Yu.S., Maksimov I V., “Feedback in a Control Problem For a System With Discontinuous Right-Hand Side”, Differ. Equ., 57:4 (2021), 533–552
Nikita Strelkovskii, Sergey Orlov, Lecture Notes in Control and Information Sciences - Proceedings, Stability, Control and Differential Games, 2020, 213
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S. M. Orlov, N. V. Strelkovskii, “Calculation of Elements of a Guiding Program Package for Singular Clusters of the Set of Initial States in the Package Guidance Problem”, Proc. Steklov Inst. Math. (Suppl.), 308, suppl. 1 (2020), S163–S177
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P. G. Surkov, “Zadacha paketnogo navedeniya s nepolnoi informatsiei pri integralnom signale nablyudeniya”, Sib. elektron. matem. izv., 15 (2018), 373–388
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Surkov P.G., “On the Problem of Package Guidance For Nonlinear Control System Via Fuzzy Approach”, IFAC PAPERSONLINE, 51:32 (2018), 733–738
Valerii Patsko, Sergey Kumkov, Varvara Turova, Handbook of Dynamic Game Theory, 2018, 1
S. M. Orlov, “Investigating One Class of Extended Open-Loop Guidance Problems”, MoscowUniv.Comput.Math.Cybern., 42:1 (2018), 5
Valerii Patsko, Sergey Kumkov, Varvara Turova, Handbook of Dynamic Game Theory, 2018, 951
N. V. Strelkovskii, S. M. Orlov, “Algorithm for Constructing a Guaranteeing Program Package in a Control Problem with Incomplete Information”, MoscowUniv.Comput.Math.Cybern., 42:2 (2018), 69
V. M. Aleksandrov, “Optimal resource consumption control of perturbed systems”, Num. Anal. Appl., 10:3 (2017), 185–197
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
Maksimov V.I., “Problem of Guaranteed Guidance By Measuring Part of the State Vector Coordinates”, Differ. Equ., 53:11 (2017), 1449–1457
Valerii Patsko, Sergey Kumkov, Varvara Turova, Handbook of Dynamic Game Theory, 2017, 1
V. M. Aleksandrov, “A singular solution to the problem of minimizing resource consumption”, Num. Anal. Appl., 9:1 (2016), 1–11
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
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