On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems

The paper is devoted to analyze the connection between turnpike phenomena and strict dissipativity properties for continuous-time finite dimensional linear quadratic optimal control problems. We characterize strict dissipativity properties of the dynamics in terms of the system matrices related to t...

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Bibliographic Details
Published inMathematical control and related fields Vol. 11; no. 1; pp. 169 - 188
Main Authors Grüne, Lars, Guglielmi, Roberto
Format Journal Article
LanguageEnglish
Published 01.03.2021
Subjects
dissipativity
long time behaviour
turnpike property
linear-quadratic optimal control
Lyapunov matrix inequality
detectability
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ISSN2156-8499
2156-8472
DOI10.3934/mcrf.2020032

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Summary:The paper is devoted to analyze the connection between turnpike phenomena and strict dissipativity properties for continuous-time finite dimensional linear quadratic optimal control problems. We characterize strict dissipativity properties of the dynamics in terms of the system matrices related to the linear quadratic problem. These characterizations then lead to new necessary conditions for the turnpike properties under consideration, and thus eventually to necessary and sufficient conditions in terms of spectral criteria and matrix inequalities. One of the key novelty of these results is the possibility to encompass the presence of state and input constraints.
ISSN:2156-8499
2156-8472
DOI:10.3934/mcrf.2020032