An investigation of optimality and controllability for quasilinear impulsive evolution systems in abstract spaces

Abstract

Abstract This paper presents the controllability and optimal control results for a structure with quasi-linear evolution in abstract spaces. First, the analytic semigroup theory was used to prove the existence and uniqueness of the quasilinear system. Additionally, the same system’s controllability outcome was examined. The latter uses fixed-point theorems to determine the best control for the quasi-linear system. Two specific examples are then provided to demonstrate the usefulness of our primary findings.

Keywords

• Controllability
• Optimal control
• Quasilinear evolution system
• Semigroup theory