Approximate controllability of semi-linear stochastic integro-differential equations with infinite delay. (18th February 2020)

• Record Type: Journal Article
• Authors: Huang, Hai; Fu, Xianlong
• Is Part Of: IMA journal of mathematical control and information. Volume 37:Number 4(2020)
• Page Start: 1133
• Page End: 1167
• Publication Date: 2020-02-18
• Subjects: stochastic integro-differential equation -- approximate controllability -- resolvent operator -- fundamental solution -- infinite delay; Control theory -- Periodicals; 629.831205
• DOI: 10.1093/imamci/dnz040
• Languages: English
• ISSNs: 0265-0754

Abstract

Abstract: In this work, by constructing fundamental solutions and using the theory of resolvent operators and fractional powers of operators, we study the approximate controllability of a class of semi-linear stochastic integro-differential equations with infinite delay in $L_p$ space ($2<p<\infty $ ). Sufficient conditions for approximate controllability of the discussed equations are obtained under the assumption that the associated deterministic linear system is approximately controllable. An example is provided to illustrate the obtained results.