Affiliation:
1. School of Basic and Applied Sciences, Department of Mathematics Harcourt Butler Technical University Kanpur‐208002 Uttar Pradesh India
2. Department of Applied Sciences Rajkiya Engineering College Kannauj Kannauj Uttar Pradesh India
Abstract
AbstractIn the framework of a second‐order semilinear integro‐differential control system in Hilbert spaces, the paper provides sufficient conditions for proving the existence of optimal control. The Banach fixed point theorem is used to investigate the existence and uniqueness of mild solutions for the proposed problem. Additionally, it is shown that, under specific assumptions, there exists at least one optimal control pair for the Lagrange's problem as presented in the article. An example for validation is included in the paper to further support the theoretical findings.
Funder
Science and Engineering Research Board