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Strict Bounded Real Decentralized Coherent Quantum Robust H-Infinity Control

Hendra Gunawan Harno, Ian R. Petersen

Published Aug 28, 2011• 0 citations
OpenAlex

Abstract

Abstract: We present a systematic method to synthesize a decentralized coherent quantum robust H controller for a class of large-scale linear complex quantum stochastic systems with norm-bounded structured uncertainties. The H control objective is to obtain a closed loop uncertain quantum system, which is strict bounded real with a specified disturbance attenuation level. The solution to this quantum control problem involves stabilizing solutions to parameterized complex Riccati equations.

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Abstract: We present a systematic method to synthesize a decentralized coherent quantum robust H controller for a class of large-scale linear complex quantum stochastic systems with norm-bounded structured uncertainties. The H control objective is to obtain a closed loop uncertain quantum system, which is strict bounded real with a specified disturbance attenuation level. The solution to this quantum control problem involves stabilizing solutions to parameterized complex Riccati equations.
This paper presents a procedure to synthesize a decentralized coherent robust H∞quantum controller for a class of large-scale uncertain linear complex quantum stochastic systems with a norm-bounded unstructured uncertainty. The H∞control objective is to obtain a strictly bounded real closed loop uncertain quantum system with a specified disturbance attenuation level g > 0. The main idea is that instead of treating the interconnections between quantum subsystems as uncertainties, we consider the neglected off-diagonal blocks of the transfer function matrix of the corresponding non-decentralized quantum controller as additional uncertainties. The resulting decentralized coherent quantum controller is required to satisfy a physical realizability condition.
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.
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.
We consider classical estimators for a class of physically realizable linear quantum systems. Optimal estimation using a complex Kalman filter for this problem has been previously explored. Here, we study robust H∞ estimation for uncertain linear quantum systems. The estimation problem is solved by converting it to a suitably scaled H∞ control problem. The solution is obtained in the form of two algebraic Riccati equations. Relevant examples involving dynamic squeezers are presented to illustrate the efficacy of our method. Copyright © 2016 John Wiley & Sons, Ltd.
Coherent feedback H∞H^\inftyH∞ control of quantum linear systems
The purpose of this paper is to investigate the coherent feedback H∞H^\inftyH∞ control problem for linear quantum systems. A key contribution is a simplified design methodology that guarantees closed-loop stability and a prescribed level of disturbance attenuation. It is shown that for general linear quantum systems, a physically realizable quantum controller can be obtained by solving at most four Lyapunov equations. In the passive case, a necessary and sufficient condition is provided in terms of two uncoupled pairs of Lyapunov equations. These results represent a significant simplification over the standard approach, which requires solving two coupled algebraic Riccati equations. The effectiveness of the proposed method is demonstrated through two typical quantum optical devices: an empty optical cavity and a degenerate parametric amplifier. These results provide a computationally efficient procedure for the robust and optimal control of quantum optical and optomechanical systems.