1 research outputs found
Frequency-domain computation of quadratic-exponential cost functionals for linear quantum stochastic systems
This paper is concerned with quadratic-exponential functionals (QEFs) as
risk-sensitive performance criteria for linear quantum stochastic systems
driven by multichannel bosonic fields. Such costs impose an exponential penalty
on quadratic functions of the quantum system variables over a bounded time
interval, and their minimization secures a number of robustness properties for
the system. We use an integral operator representation of the QEF, obtained
recently, in order to compute its asymptotic infinite-horizon growth rate in
the invariant Gaussian state when the stable system is driven by vacuum input
fields. The resulting frequency-domain formulas express the QEF growth rate in
terms of two spectral functions associated with the real and imaginary parts of
the quantum covariance kernel of the system variables. We also discuss the
computation of the QEF growth rate using homotopy and contour integration
techniques and provide two illustrations including a numerical example with a
two-mode oscillator.Comment: 8 pages, 3 figures, submitted to the 21st IFAC World Congress,
Berlin, Germany, July 12-17, 202