Faulwasser, Timm ; Grüne, Lars ; Humaloja, Jukka-Pekka ; Schaller, Manuel: The interval turnpike property for adjoints.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2020
. - 22 p.

Specialized Adaptive Algorithms for Model Predictive Control of PDEs

GR 1569/17-1

Specialized Adaptive Algorithms for Model Predictive Control of PDEs

SCHI 1379/5-1

The research was conducted while the third author was visiting University of Bayreuth under Academy of Finland Grant number 310489 held by Lassi Paunonen and supported by a travel grantfrom the Magnus Ehrnrooth Foundation

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Deutsche Forschungsgemeinschaft

Abstract in another language

In this work we derive an interval turnpike result for adjoints of finite- and infinite-dimensional nonlinear optimal control problems under the assumption of an interval turnpike on states and controls. We consider stabilizable dynamics governed by a generator of a semigroup with finite-dimensional unstable part satisfying a spectral decomposition condition and show the desired turnpike property under continuity assumptions on the first-order optimality conditions. We further give stronger estimates for analytic semigroups and provide a numerical example with a boundary controlled semilinear heat equation to illustrate the results.