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IEEE Conference on Decision and Control (CDC)

Optimal control of linear quantum systems despite feedback delay

Kazunori Nishio, Kenji Kashima, Jun‐ichi Imura

Published Jan 1, 2008• 1 citation
Publisher

Abstract

In this paper, we investigate an optimal control problem of linear quantum systems despite feedback delays. The optimal controller, which is of the Smith predictor form, and an analytical expression of the best achievable performance are derived by applying existing results for control of classical (non-quantum) I/O delay systems. Then, we analyze the performance degrading effect caused by feedback delays in an illustrative example of a quantum free particle. In particular, we give a new insight for a typical experiment setup. This is accomplished by using the performance limit expression mentioned above.

DOI
10.1109/cdc.2008.4739128

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In this paper, we investigate an optimal control problem of linear quantum systems despite feedback delays. The optimal controller, which is of the Smith predictor form, and an analytical expression of the best achievable performance are derived by applying existing results for control of classical (non-quantum) I/O delay systems. Then, we analyze the performance degrading effect caused by feedback delays in an illustrative example of a quantum free particle. In particular, we give a new insight for a typical experiment setup. This is accomplished by using the performance limit expression mentioned above.
We investigate feedback control of linear quantum systems subject to feedback-loop time delays. In particular, we examine the relation between the potentially achievable control performance and the time delays and provide theoretical guidelines for the future experimental setup in two physical systems, which are typical in this research field. The evaluation criterion for the analysis is given by the optimal control performance formula, the derivation of which is from the classical control theoretic results about the input-output delay systems.
In a quantum feedback control loop, it is often confronted with time delays mainly originated from the transition delay of signals, which may cause quantum feedback control systems unstable. The purpose of this paper is to deal with a problem of quantum measurement-based feedback control systems subject to feedback-loop time delays. A physical model for a quantum measurement-based feedback control system with time delay is presented for the H∞control. Fundamental properties such as dissipation, gain and stability for this model are presented and characterized using linear matrix inequalities (LMIs). A numerical procedure is proposed for H∞controller designs for our model. An example is given to illustrate our numerical procedure.
In this paper, feedback control of quantum spin systems is investigated. The quantum control scenario follows the formalism of continuous quantum measurement and quantum state estimation using the so-called stochastic master equation. In quantum feedback control implementations the state estimation is delayed, which is known to degrade the resulting control performance. As yet there are no theoretical means to take such estimation delays into consideration. In this paper we derive a stabilizing control law for two-dimensional quantum spin systems taking estimation delays into explicit account. From a control theoretic viewpoint, the obtained result is a delay-dependent stability criterion for a nonlinear stochastic switching system.
Feedback control (based on the quantum continuous measurement) of quantum systems inevitably suffers from estimation delays. In this technical note we give a delay-dependent stability criterion for a wide class of nonlinear stochastic systems including quantum spin systems. We utilize a semi-algebraic problem approach to incorporate the structure ofdensitymatrices. To show the effectiveness of the result, we derive a globally stabilizing control law for a quantum spin-1/2 systems in the face of feedback delays.
The bounded stability problem of linear mixed quantum-classical feedback control systems with time delays is investigated in this paper. The whole feedback system is composed of a quantum plant, a classical controller, and some interconnection devices. Two classes of feedback delays in the feedback loop are considered: constant delays and time-varying delays. The stability of the closed-loop systems under these two classes of time delays is analyzed by constructing different Lyapunov-Krasovskii functions and the corresponding stability criteria are derived, respectively. In particular, a weighting matrix is introduced into stability analysis and the obtained stability results are less conservative than relevant results for this class of quantum systems.