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IET Control Theory and Applications

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

Xiujuan Lu, Sen Kuang

Published Feb 1, 2019• 11 citations
Publisher

Abstract

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.

DOI
10.1049/iet-cta.2018.6183

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Coherent H∞H^{\infty}H∞ Control for Linear Quantum Systems With Uncertainties in the Interaction Hamiltonian
This work conducts robust H∞analysis for a class of quantum systems subject to perturbations in the interaction Hamiltonian. A necessary and sufficient condition for the robustly strict bounded real property of this type of uncertain quantum system is proposed. This paper focuses on the study of coherent robust H∞controller design for quantum systems with uncertainties in the interaction Hamiltonian. The desired controller is connected with the uncertain quantum system through direct and indirect couplings. A necessary and sufficient condition is provided to build a connection between the robust H∞control problem and the scaled H∞control problem. A numerical procedure is provided to obtain coefficients of a coherent controller. An example is presented to illustrate the controller design method.
In this paper, a class of uncertain quantum systems with uncertainties in the interaction Hamiltonian is connected with a coherent controller through direct and indirect couplings. The aim of the paper is to design a robust coherent stability controller to make the closed-loop system robustly mean square stable. A sufficient and necessary condition is presented to build a connection between robust control design with uncertain parameters and scaled control design without uncertain parameters. This condition is also considered for a special class of linear passive quantum systems. A numerical procedure is proposed to obtain explicit expression for parameters of the desired coherent controller using linear matrix inequality, multi-step optimization methods and physical realizability conditions.