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arXiv · 2005.12120

The interval turnpike property for adjoints

Timm Faulwasser·Lars Grüne·Jukka-Pekka Humaloja·Manuel Schaller
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Abstract

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.

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Timm Faulwasser, Lars Grüne, Jukka-Pekka Humaloja, Manuel Schaller. 2020-05-25. The interval turnpike property for adjoints. https://arxiv.org/abs/2005.12120

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