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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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Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, 268, suppl. 1, S54–S70
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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
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http://mi.mathnet.ru/eng/timm419 http://mi.mathnet.ru/eng/timm/v15/i3/p262
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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
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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
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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
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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
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Tarasov V.E., “On History of Mathematical Economics: Application of Fractional Calculus”, Mathematics, 7:6 (2019), 509
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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
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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
 
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