Lie-algebraic connections between two classes of risk-sensitive performance criteria for linear quantum stochastic systems

Date

2019

Authors

Vladimirov, Igor
Petersen, Ian
James, Matthew

Journal Title

Journal ISSN

Volume Title

Publisher

Society for Industrial and Applied Mathematics-SIAM Publications

Abstract

This paper is concerned with the original risk-sensitive performance criterion for quantum stochastic systems and its recent quadraticexponential counterpart. These functionals are of different structure because of the noncommutativity of quantum variables and have their own useful features such as tractability of evolution equations and robustness properties. We discuss a Lie algebraic connection between these two classes of cost functionals for open quantum harmonic oscillators using an apparatus of complex Hamiltonian kernels and symplectic factorizations. These results are aimed to extend useful properties from one of the classes of risk-sensitive costs to the other and develop state-space equations for computation and optimization of these criteria in quantum robust control and filtering problems.

Description

Keywords

Citation

Source

2019 Proceedings of the Conference on Control and its Applications

Type

Conference paper

Book Title

Entity type

Access Statement

Free Access via publisher website

License Rights

DOI

10.1137/1.9781611975758.6

Restricted until

2099-12-31