The null boundary controllability for the Mullins equation with periodic boundary conditions

Abstract

In this paper, we study the null controllability of the Mullins equation with the control acting on the periodic boundary. Firstly, using the duality relation between controllability and observability, we express the controllability condition in terms of the solution of the backward adjoint system. After showing the existence and uniqueness of the solution of the adjoint system, we determine the admissible initial data class since the system is not always controllable under these boundary conditions. Finally, using this spectral analysis, we reduce the null controllability problem to the moment problem and solve the problem on this admissible initial class.

Regional observability of Caputo semilinear fractional systems

“…Control theory encompasses many useful concepts for investigating dynamical systems such as controllability, observability, stability, and stabilization. See previous research [7][8][9][10] for more information about these concepts. Observability is one of the most important notions in the field of control theory; it was introduced in the sixties by Rudolf Kalman.…”