ISBN 9783843958059

978-3-8439-5805-9, Reihe Mathematik

Vicky Holfeld
New Methods for Nonlinear Inverse Problems in Vehicle Engineering

185 Seiten, Dissertation Universität Mannheim (2025), Softcover, A5

Zusammenfassung / Abstract

Inverse problems, in which unknown system inputs or parameters are inferred from observed outputs, play a central role in many scientific and engineering disciplines. In the context of nonlinear dynamical systems, such problems are often ill-posed, requiring dedicated numerical strategies to obtain stable and meaningful solutions.

This thesis contributes to the solution of inverse problems in dynamical systems formulated in an optimization-based framework. In this context, numerical methods are developed and analyzed across varying degrees of system knowledge, ranging from full (white-box) to limited (black-box) model transparency. As a guiding application, we consider a tracking problem within the vehicle engineering context, in which a road profile for a quarter-car model is reconstructed based on observed output data. This problem serves as a consistent benchmark for evaluating and discussing the proposed methods.

In the white-box setting, we present a function space Gauss-Newton method tailored to optimal control problems governed by ordinary differential equations. We derive and analyze several algorithmic variants and investigate different approaches for solving the arising subproblems. We also provide a global convergence result for the classical approach. In the black-box scenario, we explore iterative learning control (ILC) methods, including linear frequency-based ILC and its nonlinear extension using recurrent neural networks as surrogate models. These data-driven models are trained and inverted to enable input reconstruction via optimization techniques. Extensive numerical experiments validate the proposed techniques and offer a comparative assessment with respect to accuracy, convergence behavior, and computational efficiency.

Overall, this work bridges the gap between mathematical theory, system modeling, and numerical solution strategies specific to inverse problems, and their real-world applications in vehicle engineering.