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

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