2 research outputs found
Direct coupling coherent quantum observers with discounted mean square performance criteria 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.
Small-gain-theorem bounds are obtained for the back-action of the observer on
the covariance dynamics of the plant in terms of the plant-observer coupling. 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 effect. 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 Lie-algebraic
techniques, this set of equations is represented in a more explicit form for
equally dimensioned plant and observer. For a class of such observers with
autonomous estimation error dynamics, we obtain a solution of the CQF problem
and outline a homotopy method. The computation of the performance criteria and
the observer synthesis are illustrated by numerical examples.Comment: 19 pages, 5 figures; a brief conference version arXiv:1602.06498 of
this paper was presented at the IEEE 2016 Conference on Norbert Wiener in the
21st Centur
A homotopy approach to coherent quantum LQG control synthesis using discounted performance criteria
This paper is concerned with linear-quadratic-Gaussian (LQG) control for a
field-mediated feedback connection of a plant and a coherent (measurement-free)
controller. Both the plant and the controller are multimode open quantum
harmonic oscillators governed by linear quantum stochastic differential
equations. The control objective is to make the closed-loop system internally
stable and to minimize the infinite-horizon quadratic cost involving the plant
variables and the controller output subject to quantum physical realizability
(PR) constraints. This coherent quantum LQG (CQLQG) control problem, which has
been of active research interest for over ten years, does not admit a solution
in the form of separation principle and independent Riccati equations known for
its classical counterpart. We apply variational techniques to a family of
discounted CQLQG control problems parameterized by an effective time horizon.
This gives rise to a homotopy algorithm, which is initialized with a PR (but
not necessarily stabilizing) controller and aims at a locally optimal
stabilizing controller for the original problem in the limit.Comment: 12 pages, 1 figure, submitted to the International Symposium on
Mathematical Theory of Networks and Systems (24th MTNS 2020), 24-28 August
2020, Cambridge, United Kingdo