@inbook{17411,
  abstract     = {{Many dynamical systems possess symmetries, e.g. rotational and translational invariances of mechanical systems. These can be beneficially exploited in the design of numerical optimal control methods. We present a model predictive control scheme which is based on a library of precomputed motion primitives. The primitives are equivalence classes w.r.t. the symmetry of the optimal control problems. Trim primitives as relative equilibria w.r.t. this symmetry, play a crucial role in the algorithm. The approach is illustrated using an academic mobile robot example.}},
  author       = {{Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Peitz, Sebastian}},
  booktitle    = {{Advances in Dynamics, Optimization and Computation}},
  editor       = {{Junge, Oliver and Schütze, Oliver and Froyland, Gary and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}},
  isbn         = {{9783030512637}},
  issn         = {{2198-4182}},
  publisher    = {{Springer}},
  title        = {{{Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach}}},
  doi          = {{10.1007/978-3-030-51264-4_9}},
  year         = {{2020}},
}

@inbook{17994,
  abstract     = {{In this work we review the novel framework for the computation of finite dimensional invariant sets of infinite dimensional dynamical systems developed in [6] and [36]. By utilizing results on embedding techniques for infinite dimensional systems we extend a classical subdivision scheme [8] as well as a continuation algorithm [7] for the computation of attractors and invariant manifolds of finite dimensional systems to the infinite dimensional case. We show how to implement this approach for the analysis of delay differential equations and partial differential equations and illustrate the feasibility of our implementation by computing the attractor of the Mackey-Glass equation and the unstable manifold of the one-dimensional Kuramoto-Sivashinsky equation.}},
  author       = {{Gerlach, Raphael and Ziessler, Adrian}},
  booktitle    = {{Advances in Dynamics, Optimization and Computation}},
  editor       = {{Junge, Oliver and Schütze, Oliver and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}},
  isbn         = {{9783030512637}},
  issn         = {{2198-4182}},
  pages        = {{66--85}},
  publisher    = {{Springer International Publishing}},
  title        = {{{The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems}}},
  doi          = {{10.1007/978-3-030-51264-4_3}},
  volume       = {{304}},
  year         = {{2020}},
}