  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.
