Enhancing automic and optimal control systems through graphical structures

Sumati Kumari Panda; Ilyas Khan; Vijayakumar Velusamy; Shafiullah Niazai

doi:10.1038/s41598-024-53244-4

Enhancing automic and optimal control systems through graphical structures

Sci Rep. 2024 Feb 7;14(1):3139. doi: 10.1038/s41598-024-53244-4.

Authors

Sumati Kumari Panda^#¹, Ilyas Khan^#², Vijayakumar Velusamy^#³, Shafiullah Niazai^#⁴

Affiliations

¹ Department of Mathematics, GMR Institute of Technology, Rajam, Andhra Pradesh, 532127, India. mumy143143143@gmail.com.
² Department of Mathematics, College of Science Al-Zulfi, Majmaah University, 11952, Al-Majmaah, Saudi Arabia. i.said@mu.edu.sa.
³ Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, 632 014, India.
⁴ Department of Mathematics, Education Faculty, Laghman University, Mehtarlam City, Laghman, 2701, Afghanistan. shafiullahniazai@lu.edu.af.

^# Contributed equally.

Abstract

The concept of graphical structures of extended suprametric space is introduced in this study and applied to supra-graphical contractive mapping. A recursive algorithm in connection with graphical notions can be employed in adaptive systems to construct a desired output function iteratively after specific conditions are first defined to ensure the existence of the solution by use of supra-graphical contractive mapping. After analyzing the historical context and relevant outcomes, we discuss the usage of graphical structures and supra-graphical contractive mappings in the conceptual frameworks of adaptive control and optimal control systems.