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

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Grüne, Lars ; Guglielmi, Roberto:
On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems.
In: Mathematical Control and Related Fields. Bd. 11 (2021) Heft 1 . - S. 169-188.
ISSN 2156-8472
DOI: https://doi.org/10.3934/mcrf.2020032

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Abstract

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.