Linear Model Predictive Control for Schrödinger Equation

Abstract

The paper considers the finite-horizon constrained optimal control problem for Schrödinger equation with boundary controls and boundary observations. The plant is mapped from continuous to discrete time using the Cayley-Tustin transform, which preserves input-output-stability of the plant. The proposed transformation is structure and energy preserving and does not induce order reduction associated with the spatial discretization. The controller design setting leads to the finite horizon constrained quadratic regulator problem, which is easily realized and accounts in explicit manner for input and output/state constraints. The model predictive control (MPC) design is realized for Schrödinger equation and the results are illustrated with numerical simulations showing successful stabilization of Schrödinger equation with simultaneous satisfaction of input and output/state constraints.