@unpublished{BreitenbachBorzi2019,
  author    = {Breitenbach, Tim and Borz{\`i}, Alfio},
  title     = {On the SQH scheme to solve non-smooth PDE optimal control problems},
  series = {Numerical Functional Analysis and Optimization},
  journal   = {Numerical Functional Analysis and Optimization},
  doi       = {10.1080/01630563.2019.1599911},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-180936},
  year      = {2019},
  abstract  = {A sequential quadratic Hamiltonian (SQH) scheme for solving different classes of non-smooth and non-convex PDE optimal control problems is investigated considering seven different benchmark problems with increasing difficulty. These problems include linear and nonlinear PDEs with linear and bilinear control mechanisms, non-convex and discontinuous costs of the controls, L\(^1\) tracking terms, and the case of state constraints. The SQH method is based on the characterisation of optimality of PDE optimal control problems by the Pontryagin's maximum principle (PMP). For each problem, a theoretical discussion of the PMP optimality condition is given and results of numerical experiments are presented that demonstrate the large range of applicability of the SQH scheme.},
  language  = {en}
}
@unpublished{GeiselhartGielenLazaretal.2013,
  author    = {Geiselhart, Roman and Gielen, Rob H. and Lazar, Mircea and Wirth, Fabian R.},
  title     = {An Alternative Converse Lyapunov Theorem for Discrete-Time Systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-78512},
  year      = {2013},
  abstract  = {This paper presents an alternative approach for obtaining a converse Lyapunov theorem for discrete-time systems. The proposed approach is constructive, as it provides an explicit Lyapunov function. The developed converse theorem establishes existence of global Lyapunov functions for globally exponentially stable (GES) systems and semi-global practical Lyapunov functions for globally asymptotically stable systems. Furthermore, for specific classes of sys- tems, the developed converse theorem can be used to establish non-conservatism of a particular type of Lyapunov functions. Most notably, a proof that conewise linear Lyapunov functions are non-conservative for GES conewise linear systems is given and, as a by-product, tractable construction of polyhedral Lyapunov functions for linear systems is attained.},
  subject      = {Ljapunov-Funktion},
  language  = {en}
}