• Corpus ID: 246276126

The Inverse Problem for Controlled Differential Equations

@article{Papavasiliou2022TheIP,
  title={The Inverse Problem for Controlled Differential Equations},
  author={Anastasia Papavasiliou and Theodore Papamarkou and Yang Zhao},
  journal={ArXiv},
  year={2022},
  volume={abs/2201.10300}
}

• A. Papavasiliou, Theodore Papamarkou, Yang Zhao
• Published 25 January 2022
• Mathematics
• ArXiv

We study the problem of constructing the control driving a controlled differential equation from discrete observations of the response. By restricting the control to the space of piecewise linear paths, we identify the assumptions that ensure uniqueness. The main contribution of this paper is the introduction of a novel numerical algorithm for the construction of the piecewise linear control, that converges uniformly in time. Uniform convergence is needed for many applications and it is achieved by approaching the problem through the signature representation of the paths, which allows us to work with the whole path simultaneously.