Steady-State and Periodic Exponential Turnpike Property for Optimal Control Problems in Hilbert Spaces

@article{Trlat2018SteadyStateAP,
  title={Steady-State and Periodic Exponential Turnpike Property for Optimal Control Problems in Hilbert Spaces},
  author={E. Tr{\'e}lat and Can Zhang and E. Zuazua},
  journal={SIAM J. Control. Optim.},
  year={2018},
  volume={56},
  pages={1222-1252}
}
In this work, we study the steady-state (or periodic) exponential turnpike property of optimal control problems in Hilbert spaces. The turnpike property, which is essentially due to the hyperbolic feature of the Hamiltonian system resulting from the Pontryagin maximum principle, reflects the fact that, in large control time horizons, the optimal state and control and adjoint state remain most of the time close to an optimal steady-state. A similar statement holds true as well when replacing an… Expand
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