Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Youth Academic Annual Conference of Chinese Association of Automation (YAC)

Robust H∞ control for a class of linear quantum systems with annihilation operators

Xiujuan Lu, Sen Kuang

Published May 1, 2018• 0 citations
Publisher

Abstract

This paper considers the coherent robust H∞control problem for a class of linear quantum stochastic systems, whose models can be described by the quantum stochastic differential equations in terms of annihilation operators only, where the unknown disturbances from environment and the model uncertainties in the Hamiltonian and coupling operators exist in the system dynamics. We provide a framework to deal with this class of systems, where the robust H∞control problem of the original system is first transformed into that of a scaled system via the quantum bounded real lemma, and then an H∞controller is designed to attenuate the influence of the disturbances on the performance output. In the design of the H∞controller, a pair of algebra Riccati equations are used to obtain a numerical solution of system matrices in the controller. Finally, the simulation experiments on a one-dimensional harmonic oscillator system coupled to three quantum fields verify the effectiveness of the proposed method.

DOI
10.1109/yac.2018.8406371

Related papers

Coherent $H^{\infty }$ Control for a Class of Annihilation Operator Linear Quantum Systems

Aline I. Maalouf, Ian R. Petersen

This paper considers a coherent H∞control problem for a class of linear quantum systems which can be defined by complex quantum stochastic differential equations in terms of annihilation operators only. For this class of quantum systems, a solution to the H∞control problem can be obtained in terms of a pair of complex algebraic Riccati equations. In addition, the question of physical realizability of the resulting quantum controllers is related to a bounded real property.

IEEE Transactions on Automatic Control•Jul 21, 2010•86 citations

Coherent H∞ control for a class of linear complex quantum systems

Aline I. Maalouf, Ian R. Petersen

This paper considers a coherent Hinfincontrol problem for a class of linear quantum systems which can be defined by complex quantum stochastic differential equations in terms of annihilation operators only. For this class of quantum systems, a solution to the Hinfincontrol problem can be obtained in terms of a pair of complex Riccati equations. The paper also considers complex versions of the bounded real lemma, the strict bounded real lemma and the lossless bounded real lemma. For the class of quantum systems under consideration, the question of physical realizability is related to the bounded real and lossless bounded real properties.

Proceedings of the ... American Control Conference/Proceedings of the American Control Conference•Jan 1, 2009•54 citations

Coherent H ∞ control for linear quantum passive systems with model uncertainties

Xiujuan Lu, Sen Kuang

The coherent robust control problem for a class of linear quantum passive systems with model uncertainties is considered in this study, where both the plant and the controller are described by quantum stochastic differential equations (QSDEs). In the framework of language, the model uncertainties are translated into the uncertainties in the Hamiltonian, the coupling operators, and the scattering matrices. Based on the quantum bounded real lemma, the robust controller design of the original uncertain plant is transformed into the controller design of a new scaled system without model uncertainties. Further, the latter is transformed into the solving problem of a couple of Riccati equations and therefore the numerical solutions of the coefficient matrices of QSDEs associated with the controller dynamics are obtained. Finally, numerical simulations on an optical system coupled to three optical channels are performed to verify the effectiveness of the method proposed in this study.

IET Control Theory and Applications•Feb 1, 2019•11 citations

Coherent Robust H-Infinity Control of Uncertain Linear Quantum Stochastic Systems

Chengdi Xiang, Ian R. Petersen, Daoyi Dong

This paper considers a class of uncertain linear quantum systems subject to uncertain perturbations in the system Hamiltonian. We present a method to design a coherent robust H-infinity controller so that the closed loop system is robustly stable and achieves a prescribed level of disturbance attenuation with all the admissible uncertainties. An illustrative example shows that for the given system, the method presented in this paper has improved performance over the existing quantum H-infinity control results without considering uncertainty.

arXiv:1509.02648•Sep 9, 2015•0 citations

Coherent robust H∞control of uncertain linear quantum stochastic systems

Chengdi Xiang, Ian R. Petersen, Daoyi Dong

This paper considers a class of uncertain linear quantum systems subject to uncertain perturbations in the system Hamiltonian. We present a method to design a coherent robust H∞controller so that the closed loop system is robustly stable and achieves a prescribed level of disturbance attenuation with all the admissible uncertainties.

IEEE Conference on Decision and Control (CDC)•Dec 1, 2015•4 citations

Coherent LQG control for a class of linear complex quantum systems

Aline I. Maalouf, Ian R. Petersen

This paper considers a coherent LQG control problem for a class of linear quantum systems which can be defined by complex quantum stochastic differential equations in terms of annihilation operators only. For this class of quantum systems, a method for designing an LQG controller which satisfies a physical realizability condition is developed. This result is related to a recent result on constructing strictly positive real LQG controllers. The main idea of the paper involves constructing a suitable cost function for the LQG problem such that a physically realizable controller is obtained. The resulting controller provides robust stability as well as optimal performance.

European Control Conference (ECC)•Aug 1, 2009•20 citations
This paper considers the coherent robust H∞control problem for a class of linear quantum stochastic systems, whose models can be described by the quantum stochastic differential equations in terms of annihilation operators only, where the unknown disturbances from environment and the model uncertainties in the Hamiltonian and coupling operators exist in the system dynamics. We provide a framework to deal with this class of systems, where the robust H∞control problem of the original system is first transformed into that of a scaled system via the quantum bounded real lemma, and then an H∞controller is designed to attenuate the influence of the disturbances on the performance output. In the design of the H∞controller, a pair of algebra Riccati equations are used to obtain a numerical solution of system matrices in the controller. Finally, the simulation experiments on a one-dimensional harmonic oscillator system coupled to three quantum fields verify the effectiveness of the proposed method.
Coherent H∞H^{\infty }H∞ Control for a Class of Annihilation Operator Linear Quantum Systems
This paper considers a coherent Hinfincontrol problem for a class of linear quantum systems which can be defined by complex quantum stochastic differential equations in terms of annihilation operators only. For this class of quantum systems, a solution to the Hinfincontrol problem can be obtained in terms of a pair of complex Riccati equations. The paper also considers complex versions of the bounded real lemma, the strict bounded real lemma and the lossless bounded real lemma. For the class of quantum systems under consideration, the question of physical realizability is related to the bounded real and lossless bounded real properties.
The coherent robust control problem for a class of linear quantum passive systems with model uncertainties is considered in this study, where both the plant and the controller are described by quantum stochastic differential equations (QSDEs). In the framework of language, the model uncertainties are translated into the uncertainties in the Hamiltonian, the coupling operators, and the scattering matrices. Based on the quantum bounded real lemma, the robust controller design of the original uncertain plant is transformed into the controller design of a new scaled system without model uncertainties. Further, the latter is transformed into the solving problem of a couple of Riccati equations and therefore the numerical solutions of the coefficient matrices of QSDEs associated with the controller dynamics are obtained. Finally, numerical simulations on an optical system coupled to three optical channels are performed to verify the effectiveness of the method proposed in this study.
This paper considers a class of uncertain linear quantum systems subject to uncertain perturbations in the system Hamiltonian. We present a method to design a coherent robust H-infinity controller so that the closed loop system is robustly stable and achieves a prescribed level of disturbance attenuation with all the admissible uncertainties. An illustrative example shows that for the given system, the method presented in this paper has improved performance over the existing quantum H-infinity control results without considering uncertainty.
This paper considers a coherent LQG control problem for a class of linear quantum systems which can be defined by complex quantum stochastic differential equations in terms of annihilation operators only. For this class of quantum systems, a method for designing an LQG controller which satisfies a physical realizability condition is developed. This result is related to a recent result on constructing strictly positive real LQG controllers. The main idea of the paper involves constructing a suitable cost function for the LQG problem such that a physically realizable controller is obtained. The resulting controller provides robust stability as well as optimal performance.