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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Volume 15, Number 3, Pages 262–278
(Mi timm419)
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This article is cited in 27 scientific papers (total in 27 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.
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
Linking options:
https://www.mathnet.ru/eng/timm419 https://www.mathnet.ru/eng/timm/v15/i3/p262
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