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

The coherent robust $H^\infty $H∞ 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 $(\boldsymbol {S,L,H})...

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Bibliographic Details
Published in:IET control theory & applications Vol. 13; no. 5; pp. 711 - 720
Main Authors: Lu, Xiujuan, Kuang, Sen
Format: Journal Article
Language:English
Published: The Institution of Engineering and Technology 01.03.2019
Subjects:
coefficient matrices
coherent robust H∞ controller design
control system synthesis
controller dynamics
coupling operators
differential equations
discrete systems
H∞ control
linear quantum passive systems
linear systems
matrix algebra
model uncertainties
numerical simulation
numerical solution
optical channels
optical system
quantum stochastic differential equations
quantum theory
Research Article
Riccati equations
robust control
scaled system
scattering matrices
stochastic processes
stochastic systems
uncertain systems
coherent robust H∞ controller design
discrete systems
coupling operators
controller dynamics
differential equations
H∞ control
optical system
stochastic systems
robust control
model uncertainties
stochastic processes
numerical simulation
scattering matrices
uncertain systems
quantum theory
control system synthesis
linear systems
coefficient matrices
matrix algebra
quantum stochastic differential equations
numerical solution
linear quantum passive systems
Riccati equations
optical channels
scaled system
ISSN:1751-8644, 1751-8652
Online Access:Get full text
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Summary:The coherent robust $H^\infty $H∞ 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 $(\boldsymbol {S,L,H})$(S,L,H) 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 $H^\infty $H∞ 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.
ISSN:1751-8644
1751-8652
DOI:10.1049/iet-cta.2018.6183