Approximate controllability for semilinear second-order stochastic evolution systems with infinite delay. Issue 7 (2nd July 2020)

• Record Type: Journal Article
• Authors: Su, Xiaofeng; Fu, Xianlong
• Is Part Of: International journal of control. Volume 93:Issue 7(2020)
• Page Start: 1558
• Page End: 1569
• Publication Date: 2020-07-02
• Subjects: Second-order stochastic evolution system -- approximate controllability -- fundamental solution -- cosine operator -- infinite delay; 34K30 -- 34K35 -- 60H15 -- 60G99 -- 93C10; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2018.1518597
• Languages: English
• ISSNs: 0020-7179

Abstract

ABSTRACT: In this work, we study the approximate controllability for a class of semilinear second-order stochastic evolution systems with infinite delay. The main technique is the fundamental solution theory constructed through Laplace transformation. Some sufficient conditions for the approximate controllability result is obtained via the so-called resolvent condition and cosine family of linear operators. Duo to the fundamental solution theory applied, the nonlinear terms are only required to be partly uniformly bounded. Finally, an example is provided to illustrate the obtained results.