Minimum Relative Entropy State Transitions in Linear Stochastic Systems:  the Continuous Time Case

Igor Vladimirov; Ian Petersen

Minimum Relative Entropy State Transitions in Linear Stochastic Systems: the Continuous Time Case

Research output: Contribution to conference › Paper › peer-review

Abstract

This paper develops a dissipativity theory for
dynamical systems governed by linear Itˆo stochastic differential
equations driven by random noise with an uncertain drift. The
deviation of the noise from a standard Wiener process in the
nominal model is quantified by relative entropy. The paper
discusses a dissipation inequality for the noise relative entropy
supply. The problem of minimizing the supply required to drive
the system between given Gaussian state distributions over a
specified time horizon is considered. This problem, known in the
literature as the Schr¨odinger bridge, was treated previously in
the context of reciprocal processes. The paper obtains a closed-
form smooth solution to a Hamilton-Jacobi equation for the
minimum required relative entropy supply by using nonlinear
algebraic techniques.

Original language	English
Pages	51-58
Number of pages	8
Publication status	Published - Jul 2010
Event	International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010): Mathematics - a key technology in the 21st century - University Congress Center, Budapest, Hungary Duration: 5 Jan 2010 → 9 Jan 2010 https://www.conferences.hu/mtns2010/

Conference

Conference	International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010)
Country/Territory	Hungary
City	Budapest
Period	5/01/10 → 9/01/10
Other	The 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010) will take place at ELTE – University Congress Center, in Budapest, Hungary, between 5-9 July 2010. The Symposium is hosted by Eötvös Loránd University (ELTE) and MTA SZTAKI (Computer and Automation Research Institute, Hungarian Academy of Sciences). MTNS 2010 is a prime conference in the general area of mathematical systems theory. The symposium is interdisciplinary and attracts mathematicians, engineers and researchers working in any aspect of system theory and its applications. MTNS traditionally covers areas involving a wide range of research directions in mathematical systems, networks and control theory, with emphasis on new challenges and potential applications. A prime objective of the MTNS 2010 Symposium is to explore and present mathematics as a key technology for the 21st century.
Internet address	https://www.conferences.hu/mtns2010/

Cite this

@conference{c40df67e9bdc4a2890a4c1d384d241b2,

title = "Minimum Relative Entropy State Transitions in Linear Stochastic Systems: the Continuous Time Case",

abstract = "This paper develops a dissipativity theory for dynamical systems governed by linear Itˆo stochastic differential equations driven by random noise with an uncertain drift. The deviation of the noise from a standard Wiener process in the nominal model is quantified by relative entropy. The paper discusses a dissipation inequality for the noise relative entropy supply. The problem of minimizing the supply required to drive the system between given Gaussian state distributions over a specified time horizon is considered. This problem, known in the literature as the Schr¨odinger bridge, was treated previously in the context of reciprocal processes. The paper obtains a closed- form smooth solution to a Hamilton-Jacobi equation for the minimum required relative entropy supply by using nonlinear algebraic techniques.",

author = "Igor Vladimirov and Ian Petersen",

year = "2010",

month = jul,

language = "English",

pages = "51--58",

note = "International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010) : Mathematics - a key technology in the 21st century ; Conference date: 05-01-2010 Through 09-01-2010",

url = "https://www.conferences.hu/mtns2010/",

}

TY - CONF

T1 - Minimum Relative Entropy State Transitions in Linear Stochastic Systems

T2 - International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010)

AU - Vladimirov, Igor

AU - Petersen, Ian

PY - 2010/7

Y1 - 2010/7

N2 - This paper develops a dissipativity theory for dynamical systems governed by linear Itˆo stochastic differential equations driven by random noise with an uncertain drift. The deviation of the noise from a standard Wiener process in the nominal model is quantified by relative entropy. The paper discusses a dissipation inequality for the noise relative entropy supply. The problem of minimizing the supply required to drive the system between given Gaussian state distributions over a specified time horizon is considered. This problem, known in the literature as the Schr¨odinger bridge, was treated previously in the context of reciprocal processes. The paper obtains a closed- form smooth solution to a Hamilton-Jacobi equation for the minimum required relative entropy supply by using nonlinear algebraic techniques.

AB - This paper develops a dissipativity theory for dynamical systems governed by linear Itˆo stochastic differential equations driven by random noise with an uncertain drift. The deviation of the noise from a standard Wiener process in the nominal model is quantified by relative entropy. The paper discusses a dissipation inequality for the noise relative entropy supply. The problem of minimizing the supply required to drive the system between given Gaussian state distributions over a specified time horizon is considered. This problem, known in the literature as the Schr¨odinger bridge, was treated previously in the context of reciprocal processes. The paper obtains a closed- form smooth solution to a Hamilton-Jacobi equation for the minimum required relative entropy supply by using nonlinear algebraic techniques.

UR - https://www.conferences.hu/mtns2010/

M3 - Paper

SP - 51

EP - 58

Y2 - 5 January 2010 through 9 January 2010

ER -

Minimum Relative Entropy State Transitions in Linear Stochastic Systems: the Continuous Time Case

Abstract

Conference

Other files and links

Fingerprint

Cite this