Optimal control problem for fractional stochastic delayed systems with noninstantaneous impulses. (25th May 2021)

• Record Type: Journal Article
• Authors: Kumar, Surendra; Upadhyay, Anjali
• Is Part Of: IMA journal of mathematical control and information. Volume 38:Number 3(2021)
• Page Start: 855
• Page End: 880
• Publication Date: 2021-05-25
• Subjects: fractional Brownian motion -- fractional stochastic differential equation -- infinite delay -- noninstantaneous impulses -- mild solution -- fixed point theory; Control theory -- Periodicals; 629.831205
• DOI: 10.1093/imamci/dnab014
• Languages: English
• ISSNs: 0265-0754

Abstract

Abstract: This article investigates the existence of a solution for a class of fractional delayed stochastic differential equations with noninstantaneous impulses and fractional Brownian motion (fBm). Utilizing the theory of fractional calculus, stochastic integrals for fBm and fixed-point technique, we obtain the solvability result for the considered system. Next, we formulate a fractional stochastic optimal control problem for the infinite delayed impulsive system. Finally, the existence of an optimal state-control pair is established using the Balder Theorem. An example is also constructed that exhibits the efficiency of our results.