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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},
}