10.18453/rosdok_id00005785 Kruse, Niklas Niklas Kruse http://d-nb.info/gnd/1418844578 https://orcid.org/0000-0002-6535-8375 Universität Rostock 2026 510 Mathematics 2026 en https://purl.uni-rostock.de/rosdok/id00005785 urn:nbn:de:gbv:28-rosdok_id00005785-1 This work proposes methods for the stabilization of unstable periodic orbits by dynamically adjusting a system parameter. In particular, the case where the equations of motion of the system that possesses periodic orbits are unknown is discussed. First, a stabilization scheme based on a linear state feedback of a Poincaré map is presented. Furthermore, a data-driven nonlinear control scheme that leads to a large basin of attraction of the stabilized periodic orbit is proposed. The presented methods are numerically validated on both autonomous and non-autonomous nonlinear dynamical systems.