Approximation and convergence analysis of optimal control for non-instantaneous impulsive fractional evolution hemivariational inequalities

• Published in: Results in control and optimization Vol. 9; p. 100182
• Main Authors: Durga, N., Muthukumar, P., Niezabitowski, Michal
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2022; Elsevier
• Subjects: Approximation; Clarke’s subdifferential; Convergence; Fractional differential inclusion; Fractional optimal control; Non-instantaneous impulses; 34K40; Fractional optimal control; Approximation; 45L05; Non-instantaneous impulses; Clarke’s subdifferential; 49N25; Fractional differential inclusion; 34A08; Convergence
• ISSN: 2666-7207; 2666-7207
• DOI: 10.1016/j.rico.2022.100182

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. •Solvability and convergence results are obtained for proposed model in Hilbert space•Introduced the lower-dimensional approximations for the proposed system•Investigated the uniform convergence of solution on a compact subset of control space•Existence of fractional optimal control as Lagrange’s problem is developed•A remarkable application of PDE model is given for obtained novel theoretical results.