Effects of time delay in feedback control of linear quantum systems

和記 西尾, Nishio, Kazunori, 健司 加嶋 +3 more

Shi Wang, M. R. James

健司 加嶋, Kenji KASHIMA, 山本, 直樹 +1 more

K. Nishio, Kenji Kashima, Jun‐ichi Imura

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.

Kazunori Nishio, Kenji Kashima, Jun‐ichi Imura

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.

Shi Wang, Qing Zhong Gao, Daoyi Dong

Time delay is frequently encountered in practical quantum feedback control systems with long transmission lines and measurement process. This paper is concerned with measurement-based feedback H∞ control for quantum systems with time delays appearing in the feedback loops. A physical model is presented for the quantum time-delay system described by complex quantum stochastic differential equations. Quantum versions of some fundamental properties, such as dissipativity and stability, are discussed for this model. A numerical procedure is proposed for H∞ controller synthesis, which can deal with a non-convex optimization problem arising in the design processes. Copyright © 2016 John Wiley & Sons, Ltd.