Deep polytopic autoencoders for low-dimensional linear parameter-varying approximations and nonlinear feedback design
<|reference_start|>Deep polytopic autoencoders for low-dimensional linear parameter-varying approximations and nonlinear feedback design: Polytopic autoencoders provide low-dimensional parametrizations of states in a polytope. For nonlinear PDEs, this is readily applied to low-dimensional linear parameter-varying (LPV) approximations as they have been exploited for efficient nonlinear controller design via series expansions of the solution to the state-dependent Riccati equation. In this work, we develop a polytopic autoencoder for control applications and show how it outperforms standard linear approaches in view of LPV approximations of nonlinear systems and how the particular architecture enables higher order series expansions at little extra computational effort. We illustrate the properties and potentials of this approach to computational nonlinear controller design for large-scale systems with a thorough numerical study.<|reference_end|>
@article{heiland2024deep,
    title={Deep polytopic autoencoders for low-dimensional linear parameter-varying
  approximations and nonlinear feedback design},
    author={Jan Heiland, Yongho Kim, Steffen W. R. Werner},
    journal={arXiv preprint arXiv:2403.18044},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.18044},
    primaryClass={math.OC cs.LG cs.NA math.DS math.NA physics.flu-dyn}
}