Controllability for Semilinear Functional Integrodifferential Equations

Abstract

Abstract. This paper deals with the regularity properties for a class of semilinear integrodifferential functional differential equations. It is shown the relation between the reachable set of the semilinear system and that of its corresponding linear system. We also show that the Lipschitz continuity and the uniform boundedness of the nonlinear term can be considerably weakened. Finally, a simple example to which our main result can be applied is given.

The monotone method for controllability of the nonlinear evolution systems

“…The authors of Refs [3] and [13] studied the local controllability of a completely nonlinear system, by constructing the Fréchet derivative of f and considering the controllability of the associated linear system. In recent years, many authors investigated extensively the controllability for systems governed by the semilinear differential and functional differential inclusions in infinite-dimensional Banach spaces by using fixed point theorem and Leray-Schauder theory (see [8,9,14]). The main idea is to transform the controllability problem into a fixed-point problem for an appropriate operator in a function space, often with some assumptions which must be imposed to ensure that the linear operator A(t) generates a compact semigroup.…”

Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces

“…In [17,18] the approximate controllability of first order delay control systems has been proved when nonlinear term is a function of both state function and control function by assuming that the corresponding linear system is approximately controllable. To prove the approximate controllability of first order system, with or without delay, a relation between the reachable set of a semilinear system and that of the corresponding linear system is proved in [19][20][21][22][23]. There are several papers devoted to the approximate controllability for semilinear control systems, when the nonlinear term is independent of control function [24][25][26][27].…”

Exact Controllability of Semilinear Third Order Dispersion Equation

“…(see [6,7,8] and references therein). The controllability of an abstract semilinear control system in infinite dimensional spaces is an important property and has been studied by many authors in recent past via functional analysis approach, see [9,10,11,12,13]. For the sake of brevity, we shall write V and Z for the spaces L 2 (0, 2π) and ω(x, t)dx is conserved, and in order to conserve this quantity, we define the bounded linear operator G on Z as…”