Feedback Tracking Control of Non-Markovian Quantum Systems

• Published in: IEEE transactions on control systems technology Vol. 25; no. 5; pp. 1552 - 1563
• Main Authors: Shibei Xue, Hush, Michael R., Petersen, Ian R.
• Format: Journal Article
• Language: English
• Published: IEEE 01-09-2017
• Subjects: Colored noise; Control systems; Differential equations; Feedback control; Kalman filters; linear feedback control systems; Mathematical model; non-Markovian quantum systems; quantum colored noise; Quantum entanglement; White noise; whitening quantum filter
• ISSN: 1063-6536; 1558-0865
• DOI: 10.1109/TCST.2016.2614834

In this paper, we present a feedback tracking control strategy to reject colored noise in linear non-Markovian quantum systems. This non-Markovian system is modeled as an augmented linear Markovian system, which includes a principal system to be controlled and multiancillary systems representing the effect of the internal modes of the non-Markovian environment. The colored noise generated by the multiancillary systems disturbs the principal system through a direct interaction. Based on this model, a whitening quantum filter can be obtained for estimating the dynamical variables of both the principal and multiancillary systems, which can be used for feedback control. To reject the colored noise, a linear quadratic Gaussian controller is designed to drive the dynamical variables of the principal system to track those of a reference system. In examples, we show that colored noise with both rational and nonrational spectra in linear non-Markovian quantum systems can be efficiently rejected using our tracking control strategy.