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@PHDTHESIS{Fiedler:1010170,
author = {Fiedler, Christian Martin},
othercontributors = {Trimpe, Johann Sebastian and Herty, Michael},
title = {{C}ontributions to kernel methods in systems and control},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2025-03902},
pages = {1 Online-Ressource : Illustrationen},
year = {2025},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University; Dissertation, RWTH Aachen University, 2025},
abstract = {Machine learning is increasingly used in systems and
control, which is motivated by increasingly challenging
control, simulation and analysis problems, abundant data and
computing resources, as well as impressive theoretical and
methodological advances in machine learning. The established
class of kernel methods is of particular interest in this
context, due to their rich theory, efficient and reliable
algorithms, and modularity, and indeed kernel methods are
increasingly used in systems and control. This thesis
contributes to this flourishing field, focusing on two
exemplary and complementary topics. First, many
learning-based control approaches are based on combining
uncertainty bounds for Gaussian process (GP) regression with
robust control methods. We revisit the foundations of this
domain by consolidating, improving, and carefully evaluating
the required uncertainty bounds. As an application, we
demonstrate how they can be combined with modern robust
controller synthesis, leading to learning-enhanced robust
control with rigorous control-theoretic and statistical
guarantees. We furthermore discuss a severe practical
limitation of these approaches, the a priori knowledge of an
upper bound on the reproducing kernel Hilbert space (RKHS)
norm of the target function, and propose to combine
geometric assumptions together with kernel machines as a
promising alternative. Second, we initiate a new research
direction by combining kernels with mean field limits as
appearing in kinetic theory. Motivated by learning problems
on large-scale multiagent systems, we introduce mean field
limits of kernels, and provide an extensive theory for the
resulting RKHSs. This is used in turn in the analysis of
kernel-based statistical learning in the mean field limit,
which not only is a novel form of large-scale limit in
theoretical machine learning, but provides also a solid
foundation for applications in kinetic theory. Finally,
using the theory of reproducing kernels, we establish the
first existence result for the mean field limit of very
general discrete-time multiagent systems, and use this in
mean field optimal control. In summary, in this thesis we
improve and refine existing uses of kernel methods in
systems and control, helping to consolidate the area of
learning-based control and pushing it further towards
practical applications, and we introduce novel uses of
kernels and their theory in systems and control, with many
interesting directions for future work.},
cin = {422610 / 120000},
ddc = {004},
cid = {$I:(DE-82)422610_20200514$ / $I:(DE-82)120000_20140620$},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2025-03902},
url = {https://publications.rwth-aachen.de/record/1010170},
}
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