774 research outputs found
Coherent quantum LQG control
Based on a recently developed notion of physical realizability for quantum
linear stochastic systems, we formulate a quantum LQG optimal control problem
for quantum linear stochastic systems where the controller itself may also be a
quantum system and the plant output signal can be fully quantum. Such a control
scheme is often referred to in the quantum control literature as "coherent
feedback control.'' It distinguishes the present work from previous works on
the quantum LQG problem where measurement is performed on the plant and the
measurement signals are used as input to a fully classical controller with no
quantum degrees of freedom. The difference in our formulation is the presence
of additional non-linear and linear constraints on the coefficients of the
sought after controller, rendering the problem as a type of constrained
controller design problem. Due to the presence of these constraints our problem
is inherently computationally hard and this also distinguishes it in an
important way from the standard LQG problem. We propose a numerical procedure
for solving this problem based on an alternating projections algorithm and, as
initial demonstration of the feasibility of this approach, we provide fully
quantum controller design examples in which numerical solutions to the problem
were successfully obtained. For comparison, we also consider the case of
classical linear controllers that use direct or indirect measurements, and show
that there exists a fully quantum linear controller which offers an improvement
in performance over the classical ones.Comment: 25 pages, 1 figure, revised and corrected version (mainly to Section
8). To be published in Automatica, Journal of IFAC, 200
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
Coherent Quantum Filtering for Physically Realizable Linear Quantum Plants
The paper is concerned with a problem of coherent (measurement-free)
filtering for physically realizable (PR) linear quantum plants. The state
variables of such systems satisfy canonical commutation relations and are
governed by linear quantum stochastic differential equations, dynamically
equivalent to those of an open quantum harmonic oscillator. The problem is to
design another PR quantum system, connected unilaterally to the output of the
plant and playing the role of a quantum filter, so as to minimize a mean square
discrepancy between the dynamic variables of the plant and the output of the
filter. This coherent quantum filtering (CQF) formulation is a simplified
feedback-free version of the coherent quantum LQG control problem which remains
open despite recent studies. The CQF problem is transformed into a constrained
covariance control problem which is treated by using the Frechet
differentiation of an appropriate Lagrange function with respect to the
matrices of the filter.Comment: 14 pages, 1 figure, submitted to ECC 201
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