Convex Computation of Extremal Invariant Measures of Nonlinear Dynamical Systems and Markov Processes

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F21%3A00347993" target="_blank" >RIV/68407700:21230/21:00347993 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1007/s00332-020-09658-1" target="_blank" >https://doi.org/10.1007/s00332-020-09658-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00332-020-09658-1" target="_blank" >10.1007/s00332-020-09658-1</a>

Result language

angličtina

Original language name

Convex Computation of Extremal Invariant Measures of Nonlinear Dynamical Systems and Markov Processes

Original language description

We propose a convex-optimization-based framework for computation of invariant measures of polynomial dynamical systems and Markov processes, in discrete and continuous time. The set of all invariant measures is characterized as the feasible set of an infinite-dimensional linear program (LP). The objective functional of this LP is then used to single out a specific measure (or a class of measures) extremal with respect to the selected functional such as physical measures, ergodic measures, atomic measures (corresponding to, e.g., periodic orbits) or measures absolutely continuous w.r.t. to a given measure. The infinite-dimensional LP is then approximated using a standard hierarchy of finite-dimensional semidefinite programming problems, the solutions of which are truncated moment sequences, which are then used to reconstruct the measure. In particular, we show how to approximate the support of the measure as well as how to construct a sequence of weakly converging absolutely continuous approximations. As a by-product, we present a simple method to certify the nonexistence of an invariant measure, which is an important question in the theory of Markov processes. The presented framework, where a convex functional is minimized or maximized among all invariant measures, can be seen as a generalization of and a computational method to carry out the so-called ergodic optimization, where linear functionals are optimized over the set of invariant measures. Finally, we also describe how the presented framework can be adapted to compute eigenmeasures of the Perron-Frobenius operator.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

20205 - Automation and control systems

Project

<a href="/en/project/GJ20-11626Y" target="_blank" >GJ20-11626Y: Koopman operator framework for control of complex nonlinear dynamical systems</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2021

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of nonlinear science

ISSN

0938-8974

e-ISSN

1432-1467

Volume of the periodical

31

Issue of the periodical within the volume

1

Country of publishing house

CH - SWITZERLAND

Number of pages

26

Pages from-to

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UT code for WoS article

000608016800006

EID of the result in the Scopus database

2-s2.0-85098892294