The interval turnpike property for adjoints
Optimization and Control
2020-05-26 v1 Analysis of PDEs
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.
Cite
@article{arxiv.2005.12120,
title = {The interval turnpike property for adjoints},
author = {Timm Faulwasser and Lars Grüne and Jukka-Pekka Humaloja and Manuel Schaller},
journal= {arXiv preprint arXiv:2005.12120},
year = {2020}
}