Measurement-based feedback control of linear quantum stochastic systems with quadratic-exponential criteria

TL;DR

This paper develops a risk-sensitive optimal control framework for linear quantum systems with measurement-based feedback, aiming to stabilize the system while minimizing a quadratic-exponential cost functional.

Contribution

It introduces a novel control approach combining frequency-domain analysis and variational techniques for quantum systems with classical controllers.

Findings

Derived first-order optimality conditions for controller matrices.

Established a frequency-domain representation of the QEF growth rate.

Provided a theoretical foundation for risk-sensitive quantum control design.

Abstract

This paper is concerned with a risk-sensitive optimal control problem for a feedback connection of a quantum plant with a measurement-based classical controller. The plant is a multimode open quantum harmonic oscillator driven by a multichannel quantum Wiener process, and the controller is a linear time invariant system governed by a stochastic differential equation. The control objective is to stabilize the closed-loop system and minimize the infinite-horizon asymptotic growth rate of a quadratic-exponential functional (QEF) which penalizes the plant variables and the controller output. We combine a frequency-domain representation of the QEF growth rate, obtained recently, with variational techniques and establish first-order necessary conditions of optimality for the state-space matrices of the controller.