Optimal control problem with an integral equation as the control object

Filatova, Darya; Grzywaczewski, M.; Osmolovskii, Nikolay

doi:10.1016/j.na.2009.08.008

Cited by 12 publications

(4 citation statements)

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“…The stochastic differential equation with fractional Brownian motion was used as the mathematical model describing the economic situation x j (t). Taking into account the theoretical results proposed by Filatova et al (2010) the necessary optimality conditions were formulated. Since the real economic situation is more complex, the incorporation of the market uncertainty would allow to check the reaction (a kind of sensitivity) of the economic situation.…”

Section: Optimal Cooperation Problemmentioning

confidence: 99%

Industrial Group Production Program under Market Uncertainty

Bochnacka¹

2018

MATHMOD 2018 Extended Abstract Volume

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Section: Optimal Cooperation Problemmentioning

confidence: 99%

Industrial Group Production Program under Market Uncertainty

Bochnacka¹

2018

MATHMOD 2018 Extended Abstract Volume

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“…Thus, the increment of time of the dynamics of the system is not dx but (dx) α . For more on the subject see, e.g., [3,16,25,27,28].…”

Section: Preliminaries On Jumarie's Riemann-liouville Derivativementioning

confidence: 99%

Fractional variational calculus for nondifferentiable functions

Almeida

Torres²

2011

Computers & Mathematics with Applications

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We prove necessary optimality conditions, in the class of continuous functions, for variational problems defined with Jumarie's modified Riemann-Liouville derivative. The fractional basic problem of the calculus of variations with free boundary conditions is considered, as well as problems with isoperimetric and holonomic constraints.Comment: Submitted 13-Aug-2010; revised 24-Nov-2010; accepted 28-March-2011; for publication in Computers and Mathematics with Application

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“…Using the integration role (23) the ordinary fractional differential equation (40) can be rewritten as www.intechopen.com of numerical algorithm for the system (45), (48) are presented in (Filatova et al, 2010), that gives following optimal control (see Fig. 6).…”

Section: Setting In the Eulermentioning

confidence: 99%