Controllability of stochastic semilinear functional differential equations in Hilbert spaces

Dauer, Jerald P.; Mahmudov, Nazım I.

doi:10.1016/j.jmaa.2003.09.069

Cited by 90 publications

(40 citation statements)

References 17 publications

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“…Let us consider the special case of the system (1), which is defined in Hilbert spaces and investigated in [76]. Substituting g (t, s, X s ) = 0 in equation (1) we obtain the following state equation:…”

Section: The Stochastic Partial Differential Equations With Finite Dementioning

confidence: 99%

“…(2) is defined as follows: Definition 4 [76]. A stochastic process X is said to be a mild solution of the system (2) if the following conditions are satisfied:…”

Section: The Stochastic Partial Differential Equations With Finite Dementioning

confidence: 99%

“…The proof of Theorem 3 can be found in [76] and it is based on the application of the contraction theorem.…”

Section: Banach Fixed-point Theorem In Semilinear Controllability Promentioning

confidence: 99%

See 2 more Smart Citations

Banach fixed-point theorem in semilinear controllability problems – a survey

Klamka

Babiarz

Niezabitowski

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. The main aim of this article is to review the existing state of art concerning the complete controllability of semilinear dynamical systems. The study focus on obtaining the sufficient conditions for the complete controllability for various systems using the Banach fixedpoint theorem. We describe the results for stochastic semilinear functional integro-differential system, stochastic partial differential equations with finite delays, semilinear functional equations, a stochastic semilinear system, a impulsive stochastic integro-differential system, semilinear stochastic impulsive systems, an impulsive neutral functional evolution integro-differential system and a nonlinear stochastic neutral impulsive system. Finally, two examples are presented.

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Section: The Stochastic Partial Differential Equations With Finite Dementioning

confidence: 99%

“…(2) is defined as follows: Definition 4 [76]. A stochastic process X is said to be a mild solution of the system (2) if the following conditions are satisfied:…”

Section: The Stochastic Partial Differential Equations With Finite Dementioning

confidence: 99%

See 1 more Smart Citation

Banach fixed-point theorem in semilinear controllability problems – a survey

Klamka

Babiarz

Niezabitowski

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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“…There are lots of publications working on control problems of various systems [1][2][3][4]. Complete controllability means the systems can be steered to arbitrary final state while the systems with approximate controllability just can be steered to a small neighborhood of the final state.…”

Section: Introductionmentioning

confidence: 99%

Controllability of a stochastic functional differential equation driven by a fractional Brownian motion

Han

Yan

2018

Adv Differ Equ

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Let U, V and W be three Hilbert spaces and let B H be a W-valued fractional Brownian motion with Hurst index H ∈ ( 1 2 , 1). In this paper, we consider the approximate controllability of the Sobolev-type fractional stochastic differential equationwhere c D α is the Caputo fractional derivative of order α ∈ (1 -H, 1), the time history x t : (-∞, 0] → x t (θ ) = x(t + θ ) with t > 0 belonging to the phase space B h , the control

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“…These kinds of equations appear, for example, in the theory of control and controllability for stochastic differential equations (see [4]). Controllability of stochastic differential equations in infinite spaces has been investigated by many authors, see for example [1,2,6,[11][12][13][14][15]. The main objective of this paper is to derive conditions for the approximate controllability of a semilinear BSEEs with non-Lipschitz coefficient.…”

Section: Introductionmentioning

confidence: 99%