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 Trudy Inst. Mat. i Mekh. UrO RAN, 2005, Volume 11, Number 1, Pages 225–240 (Mi timm183)

Adaptive minimax control of a pursuit process with many pursuers in discrete dynamical systems

A. F. Shorikov

Abstract: An adaptive minimax control of a pursuit process with several controlled objects whose dynamics are described by discrete recursive vector equations is considered. It is assumed that the past realizations of the control signals of objects $I_i$ ($i=1,2,…,n$) controlled by $n$ pursuers and signals containing an incomplete information about an object II controlled by an evader are known. The sets of values of all a priori unknown parameters of the dynamical systems considered are convex polyhedra in the corresponding finite-dimensional vector spaces. Under these assumptions, the problem of adaptive minimax control of the pursuit process is stated and solved. A recursive procedure for organizing a minimax pursuit control in a certain class of feasible adaptive control strategies is suggested; each step of this procedure is based on implementation of a posteriori minimax nonlinear filtering and on solution of linear and convex programming problems. The results obtained can be used in computer modeling of real-life dynamical processes and in designing optimal navigational and control devices for various transportation systems.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2005, suppl. 1, S193–S208

Bibliographic databases:
UDC: 519.83

Citation: A. F. Shorikov, “Adaptive minimax control of a pursuit process with many pursuers in discrete dynamical systems”, Dynamical systems and control problems, Trudy Inst. Mat. i Mekh. UrO RAN, 11, no. 1, 2005, 225–240; Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 1, S193–S208

Citation in format AMSBIB
\Bibitem{Sho05} \by A.~F.~Shorikov \paper Adaptive minimax control of a~pursuit process with many pursuers in discrete dynamical systems \inbook Dynamical systems and control problems \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2005 \vol 11 \issue 1 \pages 225--240 \mathnet{http://mi.mathnet.ru/timm183} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2156259} \zmath{https://zbmath.org/?q=an:05203182} \elib{http://elibrary.ru/item.asp?id=12040698} \transl \jour Proc. Steklov Inst. Math. (Suppl.) \yr 2005 \issue , suppl. 1 \pages S193--S208 

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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. Nekrasov I.V., “Mnogoshagovaya optimizatsiya diskretnogo protsessa upravleniya metodom ogranichennogo perebora vozmozhnykh sostoyanii sistemy”, Mekhatronika, avtomatizatsiya, upravlenie, 2012, no. 10, 8–14
2. A. F. Shorikov, “Minimax program control for the approach process in a two-level hierarchical discrete dynamical system”, Autom. Remote Control, 75:3 (2014), 458–469
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