Approximation and convergence analysis of optimal control for non-instantaneous impulsive fractional evolution hemivariational inequalities
In this work, a fractional evolution hemivariational inequalities driven by non-instantaneous impulses is studied. The solvability of the proposed system is obtained by fractional calculus, properties of generalized Clarke’s subdifferential and Dhage fixed point theorem. This article also presents t...
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| Format: | Article |
| Language: | English |
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Elsevier
2022-12-01
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| Series: | Results in Control and Optimization |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666720722000546 |
| _version_ | 1811295088311009280 |
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| author | N. Durga P. Muthukumar Michal Niezabitowski |
| author_facet | N. Durga P. Muthukumar Michal Niezabitowski |
| author_sort | N. Durga |
| collection | DOAJ |
| description | In this work, a fractional evolution hemivariational inequalities driven by non-instantaneous impulses is studied. The solvability of the proposed system is obtained by fractional calculus, properties of generalized Clarke’s subdifferential and Dhage fixed point theorem. This article also presents the construction of the lower-dimensional approximation system for the proposed model, and its convergence of the mild solution is obtained. Besides, by considering suitable assumptions, the local approximation and uniform convergence results are established for the proposed system’s mild solution. Furthermore, sufficient conditions for the existence of Lagrange optimal control problem and convergence analysis of optimal control for the proposed model are formulated and proved. At last, an example is given for the illustration of invented new theoretical results. |
| first_indexed | 2024-04-13T05:28:08Z |
| format | Article |
| id | doaj.art-1086f822de6749c488127dcd71348c22 |
| institution | Directory Open Access Journal |
| issn | 2666-7207 |
| language | English |
| last_indexed | 2024-04-13T05:28:08Z |
| publishDate | 2022-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Control and Optimization |
| spelling | doaj.art-1086f822de6749c488127dcd71348c222022-12-22T03:00:32ZengElsevierResults in Control and Optimization2666-72072022-12-019100182Approximation and convergence analysis of optimal control for non-instantaneous impulsive fractional evolution hemivariational inequalitiesN. Durga0P. Muthukumar1Michal Niezabitowski2Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology-Chennai Campus, Chennai 600 127, Tamil Nadu, India; Corresponding author.Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram 624 302, Tamil Nadu, IndiaFaculty of Automatic Control, Electronics and Computer Sciences, Silesian University of Technology, Akademicka 16, Gliwice 44-100, PolandIn this work, a fractional evolution hemivariational inequalities driven by non-instantaneous impulses is studied. The solvability of the proposed system is obtained by fractional calculus, properties of generalized Clarke’s subdifferential and Dhage fixed point theorem. This article also presents the construction of the lower-dimensional approximation system for the proposed model, and its convergence of the mild solution is obtained. Besides, by considering suitable assumptions, the local approximation and uniform convergence results are established for the proposed system’s mild solution. Furthermore, sufficient conditions for the existence of Lagrange optimal control problem and convergence analysis of optimal control for the proposed model are formulated and proved. At last, an example is given for the illustration of invented new theoretical results.http://www.sciencedirect.com/science/article/pii/S2666720722000546ApproximationClarke’s subdifferentialConvergenceFractional optimal controlFractional differential inclusionNon-instantaneous impulses |
| spellingShingle | N. Durga P. Muthukumar Michal Niezabitowski Approximation and convergence analysis of optimal control for non-instantaneous impulsive fractional evolution hemivariational inequalities Results in Control and Optimization Approximation Clarke’s subdifferential Convergence Fractional optimal control Fractional differential inclusion Non-instantaneous impulses |
| title | Approximation and convergence analysis of optimal control for non-instantaneous impulsive fractional evolution hemivariational inequalities |
| title_full | Approximation and convergence analysis of optimal control for non-instantaneous impulsive fractional evolution hemivariational inequalities |
| title_fullStr | Approximation and convergence analysis of optimal control for non-instantaneous impulsive fractional evolution hemivariational inequalities |
| title_full_unstemmed | Approximation and convergence analysis of optimal control for non-instantaneous impulsive fractional evolution hemivariational inequalities |
| title_short | Approximation and convergence analysis of optimal control for non-instantaneous impulsive fractional evolution hemivariational inequalities |
| title_sort | approximation and convergence analysis of optimal control for non instantaneous impulsive fractional evolution hemivariational inequalities |
| topic | Approximation Clarke’s subdifferential Convergence Fractional optimal control Fractional differential inclusion Non-instantaneous impulses |
| url | http://www.sciencedirect.com/science/article/pii/S2666720722000546 |
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