119 research outputs found
Directly Coupled Observers for Quantum Harmonic Oscillators with Discounted Mean Square Cost Functionals and Penalized Back-action
This paper is concerned with quantum harmonic oscillators consisting of a
quantum plant and a directly coupled coherent quantum observer. We employ
discounted quadratic performance criteria in the form of exponentially weighted
time averages of second-order moments of the system variables. A coherent
quantum filtering (CQF) problem is formulated as the minimization of the
discounted mean square of an estimation error, with which the dynamic variables
of the observer approximate those of the plant. The cost functional also
involves a quadratic penalty on the plant-observer coupling matrix in order to
mitigate the back-action of the observer on the covariance dynamics of the
plant. For the discounted mean square optimal CQF problem with penalized
back-action, we establish first-order necessary conditions of optimality in the
form of algebraic matrix equations. By using the Hamiltonian structure of the
Heisenberg dynamics and related Lie-algebraic techniques, we represent this set
of equations in a more explicit form in the case of equally dimensioned plant
and observer.Comment: 11 pages, a brief version to be submitted to the IEEE 2016 Conference
on Norbert Wiener in the 21st Century, 13-15 July, Melbourne, Australi
Notes on Coherent Feedback Control for Linear Quantum Systems
This paper considers some formulations and possible approaches to the
coherent LQG and quantum control problems. Some new results for
these problems are presented in the case of annihilation operator only quantum
systems showing that in this case, the optimal controllers are trivial
controllers.Comment: A preliminary version is to appear in the proceedings of the 2013
Australian Control COnferenc
Direct and Indirect Couplings in Coherent Feedback Control of Linear Quantum Systems
The purpose of this paper is to study and design direct and indirect
couplings for use in coherent feedback control of a class of linear quantum
stochastic systems. A general physical model for a nominal linear quantum
system coupled directly and indirectly to external systems is presented.
Fundamental properties of stability, dissipation, passivity, and gain for this
class of linear quantum models are presented and characterized using complex
Lyapunov equations and linear matrix inequalities (LMIs). Coherent
and LQG synthesis methods are extended to accommodate direct couplings using
multistep optimization. Examples are given to illustrate the results.Comment: 33 pages, 7 figures; accepted for publication in IEEE Transactions on
Automatic Control, October 201
A Direct Coupling Coherent Quantum Observer for a Single Qubit Finite Level Quantum System
This paper considers the problem of constructing a direct coupling quantum
observer for a single qubit finite level quantum system plant. The proposed
observer is a single mode linear quantum system which is shown to be able to
estimate one of the plant variables in a time averaged sense. A numerical
example and simulations are included to illustrate the properties of the
observer.Comment: A preliminary version of this paper has been accepted to appear in
the 2014 Australian Control Conferenc
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