An exponential turnpike property for a semilinear control problem is proved. The state-target is assumed to be small, whereas the initial datum can be arbitrary. Turnpike results are also obtained for large targets, requiring that the control acts everywhere. In this case, we prove the convergence of the infimum of the averaged time-evolution functional towards the steady one. Numerical simulations are performed.
Keywords: Optimal control problems, Long time behavior, the turnpike property, semilinear parabolic equations
@article{COCV_2021__27_1_A50_0,
author = {Pighin, Dario},
title = {The turnpike property in semilinear control},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021036},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021036/}
}
Pighin, Dario. The turnpike property in semilinear control. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 48. doi: 10.1051/cocv/2021036
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This project has received funding from the European Research Council (ERC) under the European Unionś Horizon 2020 research and innovation programme (grant agreement No 694126-DYCON).
