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Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 3, Pages 262–278 (Mi timm419)  

This article is cited in 8 scientific papers (total in 8 papers)

Game problems for fractional-order linear systems

A. A. Chikrii, I. I. Matichin

Glushkov Institute of Cybernetics NAS Ukraine

Abstract: The paper is concerned with studying approach game problems for linear conflict-controlled processes with fractional derivatives of arbitrary order. Namely, the classical Riemann–Liouville fractional derivatives, Dzhrbashyan–Nersesyan or Caputo regularized derivatives, and Miller–Ross sequential derivatives are considered. Under fixed controls of the players, solutions are presented in the form of analogs of the Cauchy formula with the use of generalized matrix Mittag-Leffler functions. The investigation is based on the method of resolving functions, which allows one to obtain sufficient conditions for the termination of the approach problem in some guaranteed time. The results are exemplified by model game problems with a simple matrix and separated motions of fractional order $\pi$and $e$.

Keywords: fractional derivative, game problem, set-valued map, Pontryagin condition, Mittag-Leffler function.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, 268, suppl. 1, S54–S70

Bibliographic databases:

UDC: 518.9
Received: 25.02.2009

Citation: A. A. Chikrii, I. I. Matichin, “Game problems for fractional-order linear systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 3, 2009, 262–278; Proc. Steklov Inst. Math. (Suppl.), 268, suppl. 1 (2010), S54–S70

Citation in format AMSBIB
\by A.~A.~Chikrii, I.~I.~Matichin
\paper Game problems for fractional-order linear systems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 3
\pages 262--278
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2010
\vol 268
\issue , suppl. 1
\pages S54--S70

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    This publication is cited in the following articles:
    1. A. A. Chikrii, I. I. Matichin, “O lineinykh konfliktno upravlyaemykh protsessakh s drobnymi proizvodnymi”, Tr. IMM UrO RAN, 17, no. 2, 2011, 256–270  mathnet  elib
    2. N. N. Petrov, “Odna zadacha gruppovogo presledovaniya s drobnymi proizvodnymi i fazovymi ogranicheniyami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:1 (2017), 54–59  mathnet  crossref  elib
    3. A. S. Bannikov, “Uklonenie ot gruppy presledovatelei v zadache gruppovogo presledovaniya s drobnymi proizvodnymi i fazovymi ogranicheniyami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:3 (2017), 309–314  mathnet  crossref  elib
    4. N. N. Petrov, “A multiple capture in a group pursuit problem with fractional derivatives”, Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S150–S157  mathnet  crossref  crossref  isi  elib
    5. Gomoyunov M.I., “Fractional Derivatives of Convex Lyapunov Functions and Control Problems in Fractional Order Systems”, Fract. Calc. Appl. Anal., 21:5 (2018), 1238–1261  crossref  isi
    6. Tarasov V.E., “On History of Mathematical Economics: Application of Fractional Calculus”, Mathematics, 7:6 (2019), 509  crossref  isi
    7. N. N. Petrov, A. Ya. Narmanov, “Mnogokratnaya poimka zadannogo chisla ubegayuschikh v zadache s drobnymi proizvodnymi i prostoi matritsei”, Tr. IMM UrO RAN, 25, no. 3, 2019, 188–199  mathnet  crossref  elib
    8. Petrov N.N., “Group Pursuit Problem in a Differential Game With Fractional Derivatives, State Constraints, and Simple Matrix”, Differ. Equ., 55:6 (2019), 841–848  crossref  mathscinet  zmath  isi  scopus
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