H^ Control of Linear Quantum Stochastic Systems

The purpose of this paper is to formulate and solve a H infin controller synthesis problem for a class of noncommutative linear stochastic systems which includes many examples of interest in quantum technology. The paper includes results on the class of such systems for which the quantum commutation...

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Vydané v:IEEE transactions on automatic control Ročník 53; číslo 8; s. 1787 - 1803
Hlavní autori: James, M.R., Nurdin, H.I., Petersen, I.R.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York, NY IEEE 01.09.2008
Institute of Electrical and Electronics Engineers
Predmet:
Applied sciences
Australia Council
Computer science; control theory; systems
Control system synthesis
Control systems
Control theory. Systems
dissipativity
Exact sciences and technology
Feedback control
Fundamental areas of phenomenology (including applications)
H^{\infty} robust control
Optical attenuators
Optical control
Optical feedback
Optics
Physics
quantum controller realization
quantum feedback control
Quantum optics
Robust control
Signal synthesis
Stochastic systems
strict bounded real lemma
Bounded real lemma
Quantum system
quantum controller realization
H∞ robust control
Hamiltonian function
strict bounded real lemma
H2 control
Necessary and sufficient condition
H infinite control
Quantum optics
Feedback regulation
Control synthesis
dissipativity
Linear control
Matrix function
Closed feedback
Robust control
Quantum computation
Uncertain system
Linear system
Non commutative algebra
Dissipative system
quantum feedback control
Riccati equation
ISSN:0018-9286, 1558-2523
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Popis
Shrnutí:The purpose of this paper is to formulate and solve a H infin controller synthesis problem for a class of noncommutative linear stochastic systems which includes many examples of interest in quantum technology. The paper includes results on the class of such systems for which the quantum commutation relations are preserved (such a requirement must be satisfied in a physical quantum system). A quantum version of standard (classical) dissipativity results are presented and from this a quantum version of the strict bounded real lemma is derived. This enables a quantum version of the two Riccati solution to the H infin control problem to be presented. This result leads to controllers which may be realized using purely quantum, purely classical or a mixture of quantum and classical elements. This issue of physical realizability of the controller is examined in detail, and necessary and sufficient conditions are given. Our results are constructive in the sense that we provide explicit formulas for the Hamiltonian function and coupling operator corresponding to the controller.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2008.929378