A mutual control problem for semilinear system via fixed point approach

TL;DR

This paper introduces a mutual control problem for semilinear systems, employing fixed point theorems and novel norm techniques to analyze control and observability issues.

Contribution

It presents a new mutual control problem framework and applies advanced fixed point theorems and norm methods for analysis.

Findings

Established existence of solutions using fixed point theorems

Developed a novel technique for semi-observability analysis

Extended control theory for semilinear systems

Abstract

In this paper, we introduce and discuss the concept of a mutual control problem. Our analysis relies on a vector fixed-point approach based on the fixed-point theorems of Perov, Schauder, Leray-Schauder, and Avramescu. Additionally, for a related semi-observability problem, we employ a novel technique utilizing Bielecki equivalent norms.