Open AccessTrajectory approximately controllability and optimal control for noninstantaneous impulsive inclusions without compactness
Author(s) -
Shengda Liu,
JinRong Wang,
Donal O’Regan
Publication year - 2021
Publication title -
topological methods in nonlinear analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.623
H-Index - 23
ISSN - 1230-3429
DOI - 10.12775/tmna.2020.069
Subject(s) - controllability , differential inclusion , mathematics , banach space , compact space , semigroup , nonlinear system , mathematical analysis , control theory (sociology) , pure mathematics , control (management) , computer science , physics , quantum mechanics , artificial intelligence
In this paper, a noninstantaneous impulsive differential inclusion model is established based on the heating phenomenon of the rod. The controllability problem for this system governed by a semilinear differential inclusion with noninstantaneous impulses is studied in a Banach space and in this differential inclusion system we assume that the semigroup generated by the linear part of the inclusion is not compact. We suppose that the set-valued nonlinearity satisfies a regularity condition expressed in terms of the Hausdorff measure of noncompactness and some sufficient conditions for approximately controllability for both upper and almost lower semicontinuous types of nonlinearity are presented. Also we discuss existence and the stability of optimal control. As an application, the controllability for a differential inclusion system governed by a heat equation is considered.