A quasi-separation principle and Newton-like scheme for coherent quantum LQG control

Abstract

This paper is concerned with the coherent quantum linear quadratic Gaussian (LQG) control problem of constructing an optimal controller for linear quantum plants using a quadratic performance criterion. Coherent quantum feedback control does not employ classical measurements which inherently entail the loss of quantum information. A coherent quantum controller is itself a quantum system and this imposes physical realizability (PR) constraints on the quantum stochastic differential equation which governs such a controller. PR corresponds to the equivalence of the controller to an open quantum harmonic oscillator whereby its state-space matrices are related to the Hamiltonian and coupling operators of the oscillator. The Hamiltonian parameterization of the controller is combined with Frechet differentiation of the LQG cost with respect to the state-space matrices in order to obtain equations for the optimal controller. A quasi-separation property for the gain matrices of the quantum controller is established, and a Newton-like iterative scheme for the numerical solution of the equations is outlined.