Control systems described by a class of fractional semilinear evolution hemivariational inequalities and their relaxation property. (3rd October 2022)

• Record Type: Journal Article
• Authors: Li, Jing; Bin, Maojun
• Is Part Of: Optimization. Volume 71:Number 10(2022)
• Page Start: 2841
• Page End: 2863
• Publication Date: 2022-10-03
• Subjects: Fractional evolution hemivariational inequalities -- relaxation property -- generalized clarke subdifferential -- feedback control -- nonconvex constraint; 49J15; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1887183
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: We are concerned with control systems described by a class of semilinear fractional evolution hemivariational inequalities in separable reflexive Banach spaces. The constraint on the control is a nonconvex valued multivalued function which is lower semicontinuous with respect to the variable states. Along with the original system we also consider the system in which the constraint on the control is the upper semicontinuous convex valued regularization of the original constraint. We obtain the existence results of the control systems and the relaxation property among the solution sets of these systems. In the end, an example is provided to illustrate the application of the obtained theory.