Feedback control of parametrized PDEs via model order reduction and dynamic programming principle

@article{Alla2020FeedbackCO,
  title={Feedback control of parametrized PDEs via model order reduction and dynamic programming principle},
  author={Alessandro Alla and Bernard Haasdonk and Andr{\'e} Schmidt},
  journal={Advances in Computational Mathematics},
  year={2020},
  volume={46},
  pages={1-28}
}
In this paper, we investigate infinite horizon optimal control problems for parametrized partial differential equations. We are interested in feedback control via dynamic programming equations which is well-known to suffer from the curse of dimensionality. Thus, we apply parametric model order reduction techniques to construct low-dimensional subspaces with suitable information on the control problem, where the dynamic programming equations can be approximated. To guarantee a low number of… 
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