Asymptotic Regional Boundary Gradient Observability in Diffusion Neumann Problem

Abstract The principle objective of this paper is to determine the concept of asymptotic regional boundary gradient observability to the case of diffusion system with Neumann boundary conditions. More precisely, for linear distributed parameter diffusion systems, we show that the sensors characterizations allow to reconstruct regional boundary gradient state in a boundary target subregion of the considered systems domain. Moreover, various interesting results associated with the selection of sensors are explained in specific and customized position situations respect to the asymptotic regional boundary gradient observability notion to be realized. Finally, we was clarified the existence of a dynamical systems that is not asymptotic boundary gradient observable in whole the boundary domain, but it may be performed on a part of boundary domain.