The role of an L_2(Omega­)-energy estimate in the theories of uniform stabilization and exact controllability for Schrödinger equations with Neumann boundary control

Abstract

The present paper deals with (linear) Schrödinger equations, of very general form, which are defined on a bounded domain ­ Omega subset R^n. With focus on these dynamics, we shall then discuss and analyze the specific and foundational topic of a-priori energy identities, with the goal of deriving control-theoretic implications. These will include the issue of optimal regularity, as well as the problems of exact controllability (by open loop controls) and of uniform stabilization (by closed loop feedback controls).

Keywords

• Schrödinger equation
• Neumann boundary control
• exact controllability
• uniform stabilization.