What is the Lagrangian for Nonlinear Filtering?

Jin Won Kim, Prashant G. Mehta, Sean P. Meyn. What is the Lagrangian for Nonlinear Filtering?. In 58th IEEE Conference on Decision and Control, CDC 2019, Nice, France, December 11-13, 2019. pages 1607-1614, IEEE, 2019. [doi]

@inproceedings{KimMM19,
  title = {What is the Lagrangian for Nonlinear Filtering?},
  author = {Jin Won Kim and Prashant G. Mehta and Sean P. Meyn},
  year = {2019},
  doi = {10.1109/CDC40024.2019.9030206},
  url = {https://doi.org/10.1109/CDC40024.2019.9030206},
  researchr = {https://researchr.org/publication/KimMM19},
  cites = {0},
  citedby = {0},
  pages = {1607-1614},
  booktitle = {58th IEEE Conference on Decision and Control, CDC 2019, Nice, France, December 11-13, 2019},
  publisher = {IEEE},
}