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

Igor G. Vladimirov; Ian R. Petersen; Matthew R. James

doi:10.1137/1.9781611975758.6

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

Igor G. Vladimirov, Ian R. Petersen, Matthew R. James

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

7 Citations (Scopus)

Abstract

This paper is concerned with the original risk-sensitive performance criterion for quantum stochastic systems and its recent quadratic-exponential 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.

Original language	English
Title of host publication	2019 Proceedings of the Conference on Control and its Applications (CT)
Editors	William S. Levine, Richard Stockbridge
Publisher	Society for Industrial and Applied Mathematics Publications
Pages	30-37
Number of pages	8
ISBN (Electronic)	9781611975758
DOIs	https://doi.org/10.1137/1.9781611975758.6
Publication status	Published - 2019
Event	2019 SIAM Conference on Control and Its Applications - Chengdu, China Duration: 19 Jun 2019 → 21 Jun 2019 https://epubs.siam.org/doi/book/10.1137/1.9781611975758

Conference

Conference	2019 SIAM Conference on Control and Its Applications
Abbreviated title	SIAM CT 2019
Country/Territory	China
City	Chengdu
Period	19/06/19 → 21/06/19
Other	The field of control theory is central to a wide range of aerospace, energy, automotive and advanced technological systems and is increasingly recognized as fundamental for emerging fields ranging from nanotechnology, smart grid to cell regulation. Moreover, in addition to its traditional ubiquity in process regulation for the physical sciences and engineering, control concepts now pervade the biological, computer, and social sciences. This conference showcases a wide range of topics in control and systems theory. The topics and applications include control of PDEs, computational mathematics for control and optimization, real-time optimization and data assimilation, cooperative control for unmanned autonomous vehicles, differential games, cellular and biological regulation, control of hybrid systems, control techniques for financial mathematics, biomedical control, risk sensitive control and filtering, control of smart systems, flow control and quantum control.
Internet address	https://epubs.siam.org/doi/book/10.1137/1.9781611975758

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10.1137/1.9781611975758.6

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Vladimirov, I. G., Petersen, I. R., & James, M. R. (2019). Lie-algebraic connections between two classes of risk-sensitive performance criteria for linear quantum stochastic systems. In W. S. Levine, & R. Stockbridge (Eds.), 2019 Proceedings of the Conference on Control and its Applications (CT) (pp. 30-37). Society for Industrial and Applied Mathematics Publications. https://doi.org/10.1137/1.9781611975758.6

Vladimirov, Igor G. ; Petersen, Ian R. ; James, Matthew R. / Lie-algebraic connections between two classes of risk-sensitive performance criteria for linear quantum stochastic systems. 2019 Proceedings of the Conference on Control and its Applications (CT). editor / William S. Levine ; Richard Stockbridge. Society for Industrial and Applied Mathematics Publications, 2019. pp. 30-37

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Vladimirov, IG , Petersen, IR & James, MR 2019, Lie-algebraic connections between two classes of risk-sensitive performance criteria for linear quantum stochastic systems. in WS Levine & R Stockbridge (eds), 2019 Proceedings of the Conference on Control and its Applications (CT). Society for Industrial and Applied Mathematics Publications, pp. 30-37, 2019 SIAM Conference on Control and Its Applications, Chengdu, China, 19/06/19. https://doi.org/10.1137/1.9781611975758.6

Lie-algebraic connections between two classes of risk-sensitive performance criteria for linear quantum stochastic systems. / Vladimirov, Igor G.; Petersen, Ian R.; James, Matthew R.
2019 Proceedings of the Conference on Control and its Applications (CT). ed. / William S. Levine; Richard Stockbridge. Society for Industrial and Applied Mathematics Publications, 2019. p. 30-37.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - This paper is concerned with the original risk-sensitive performance criterion for quantum stochastic systems and its recent quadratic-exponential 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.

AB - This paper is concerned with the original risk-sensitive performance criterion for quantum stochastic systems and its recent quadratic-exponential 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.

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Vladimirov IG , Petersen IR, James MR. Lie-algebraic connections between two classes of risk-sensitive performance criteria for linear quantum stochastic systems. In Levine WS, Stockbridge R, editors, 2019 Proceedings of the Conference on Control and its Applications (CT). Society for Industrial and Applied Mathematics Publications. 2019. p. 30-37 doi: 10.1137/1.9781611975758.6

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

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