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2021 Trajectory approximately controllability and optimal control for noninstantaneous impulsive inclusions without compactness
Shengda Liu, JinRong Wang, Donal O'Regan
Topol. Methods Nonlinear Anal. 58(1): 19-49 (2021). DOI: 10.12775/TMNA.2020.069

Abstract

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.

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Shengda Liu. JinRong Wang. Donal O'Regan. "Trajectory approximately controllability and optimal control for noninstantaneous impulsive inclusions without compactness." Topol. Methods Nonlinear Anal. 58 (1) 19 - 49, 2021. https://doi.org/10.12775/TMNA.2020.069

Information

Published: 2021
First available in Project Euclid: 21 September 2021

Digital Object Identifier: 10.12775/TMNA.2020.069

Rights: Copyright © 2021 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.58 • No. 1 • 2021
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