Stability Of Stochastic Model Predictive Control For Schrödinger Equation With Finite Approximation

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