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

Grüne Lars; Guglielmi Roberto

doi:10.3934/mcrf.2020032

Article Contents

2021, Volume 11, Issue 1: 169-188. Doi: 10.3934/mcrf.2020032

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

Grüne Lars^1, and
Guglielmi Roberto^2, ,

1.
Mathematical Institute, University of Bayreuth, Germany
2.
Institute of Applied Mathematics, Fundação Getúlio Vargas, Rio de Janeiro, Brasil

^* Corresponding author: Roberto Guglielmi
^* Corresponding author: Roberto Guglielmi

Received: November 2019

Revised: March 2020

Early access: June 2020

Published: March 2021

The first author acknowledges support from the Deutsche Forschungsgemeinschaft via Grant GR 1569/16-1. The second author was partially supported by the project INdAM-GNAMPA 2019 on "Controllabilità di PDE in modelli fisici e in scienze della vita", and he wish to thanks also the Mathematical Institute of the University of Bayreuth for supporting his visit to the department

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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.

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Mathematics Subject Classification: Primary:49K15, 49N10, 49J15, 93D20, 93C15.

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Figure 1. Schematic sketch of Theorem 8.1

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Figure 2. Schematic sketch of Theorem 8.4

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