Polytopic Autoencoders as a new model order reduction approach with applications in nonlinear controller design

Speaker:             Jan Heiland

Time:                  9:00, July. 23rd.

Location:            SIST 2-415

Host:                   Prof. Qifeng Liao

Abstract:

The controller design for both nonlinear and large-scale dynamical systems is a challenge and, up to now, no generally applicable and feasible computational approach has been established.

In this talk, we will consider approximative LPV embeddings that allow us to parametrize and reduce the system's structural complexity (so that controller design becomes easier) while leaving the state space untouched (so that the model expressiveness is preserved).

For such models with a reduced and parametrized nonlinear structure but a high-dimensional state space, several computational approaches are available for controller design. For all of them, however, a low-dimensional parametrization is important. For that we present the concept of polytopic autoencoders that reliably outperform standard model order reduction like POD (Proper Orthogonal Decomposition) at very low dimensions and that provide additional beneficial structures in the LPV parametrization. The main idea is that reconstruction happens in a polytope rather than in a linear space and the realization is done in specially developed neural network architectures.

Owing to a particular structure in the neural network design, the concept of polytopic autoencoders comes with the beneficial analytical property of preserving the exact Jacobian in the points of interest.

The general concept will be illustrated with numerical example simulations.

Bio:

Jan Heiland graduated from the TU Berlin in 2009. After a short period of work for Bombardier Transportation he started a PhD project at TU Berlin which he defended in 2014. Since then he has been a researcher and team leader at the Max Planck Institute for Dynamics of Complex Technical Systems in Magdeburg. In 2018 he was appointed Junior Professor at the Otto von Guericke University of Magdeburg and in 2021 temporary full professor for Data-driven design of dynamical systems at the FAU Erlangen/Nuremburg. Since 2024 he is with the TU Ilmenau as a lecturer. Jan Heiland's research interests include system and control theory and robust control, differential algebraic equations, infinite dimensional systems, model reduction, and design and simulation of large-scale and nonlinear control systems.