2020
DOI: 10.1002/mma.6177
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Optimal controls for second‐order stochastic differential equations driven by mixed‐fractional Brownian motion with impulses

Abstract: We study optimal control problems for a class of second‐order stochastic differential equation driven by mixed‐fractional Brownian motion with non‐instantaneous impulses. By using stochastic analysis theory, strongly continuous cosine family, and a fixed point approach, we establish the existence of mild solutions for the stochastic system. Moreover, the optimal control results are derived without uniqueness of mild solutions of the stochastic system. Finally, the main results are validated with the aid of an … Show more

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Cited by 38 publications
(33 citation statements)
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“…Remark The problems of solvability and optimal control of with impulse and without impulse fractional SDEs have been studied by many authors 25‐31 in infinite dimensional space. Till now, no literature is available in the finite dimensional space for dealing solvability and optimal control of fractional SDEs with impulsive effects.…”
Section: Examplementioning
confidence: 99%
“…Remark The problems of solvability and optimal control of with impulse and without impulse fractional SDEs have been studied by many authors 25‐31 in infinite dimensional space. Till now, no literature is available in the finite dimensional space for dealing solvability and optimal control of fractional SDEs with impulsive effects.…”
Section: Examplementioning
confidence: 99%
“…The fractional OCP refers to optimize the cost functional subject to dynamical constraints on the control parameter and state variables that having fractional models. For more recent works on OCP, see [25][26][27][28][29][30] and the references therein. Harrat et al [31] investigated the existence of optimal controls for Hilfer fractional impulsive evolution inclusions with Clarke subdifferential.…”
Section: Introductionmentioning
confidence: 99%
“…The optimal control theory has a considerable development, and one can find applications in many domains (see [9][10][11]13,33]). The time optimal control is an important topic in the theory of optimal controls and plays a vital role in control systems.…”
Section: Introductionmentioning
confidence: 99%