Stability of Stochastic Model Predictive Control for Schrödinger Equation with Finite Approximation

Recent technological advance has prompted significant
interest in developing the control theory of quantum systems.
Following the increasing interest in the control of quantum
dynamics, this paper examines the control problem of Schrödinger
equation because quantum dynamics is basically governed by
Schrödinger equation. From the practical point of view, stochastic
disturbances cannot be avoided in the implementation of control
method for quantum systems. Thus, we consider here the robust
stabilization problem of Schrödinger equation against stochastic
disturbances. In this paper, we adopt model predictive control method
in which control performance over a finite future is optimized with
a performance index that has a moving initial and terminal time.
The objective of this study is to derive the stability criterion for
model predictive control of Schrödinger equation under stochastic
disturbances.

Authors:

• Tomoaki Hashimoto

Keywords:

• Optimal control
• stochastic systems
• quantum systems
• stabilization.

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