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European Control Conference (ECC)

Coherent LQG control for a class of linear complex quantum systems

Aline I. Maalouf, Ian R. Petersen

Published Aug 1, 2009• 20 citations
Publisher

Abstract

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.

DOI
10.23919/ecc.2009.7074743

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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.
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.
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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.