Executive Summary : | Mathematical control theory plays a vital part in analyzing dynamic systems. A control system assists in obtaining the desired response by controlling various quantities present in the system. Controllability is an essential criterion for mathematical control theory and plays a significant role in many control problems such as the stabilization of unstable systems via feedback control, the irreducibility of transition semigroups, optimal control problems, etc. In general, the controllability of dynamical systems is governed by differential equations. A stronger version of approximate controllability is known as finite-approximate controllability. Finite approximate controllability indicates that the approximate control can be chosen so that the final state simultaneously satisfies the condition for approximate controllability and a finite number of constraints. In this proposal, we will focus on the finite/approximate controllability of the impulsive integrodifferential equation with delay, the Impulsive neutral evolution equation, semilinear deterministic or nondeterministic model of second-order with finite/ infinite delay. We will achieve our result by using the fixed-point technique together with the semigroup theory. |