@article{16297,
  abstract     = {{In real-world problems, uncertainties (e.g., errors in the measurement,
precision errors) often lead to poor performance of numerical algorithms when
not explicitly taken into account. This is also the case for control problems,
where optimal solutions can degrade in quality or even become infeasible. Thus,
there is the need to design methods that can handle uncertainty. In this work,
we consider nonlinear multi-objective optimal control problems with uncertainty
on the initial conditions, and in particular their incorporation into a
feedback loop via model predictive control (MPC). In multi-objective optimal
control, an optimal compromise between multiple conflicting criteria has to be
found. For such problems, not much has been reported in terms of uncertainties.
To address this problem class, we design an offline/online framework to compute
an approximation of efficient control strategies. This approach is closely
related to explicit MPC for nonlinear systems, where the potentially expensive
optimization problem is solved in an offline phase in order to enable fast
solutions in the online phase. In order to reduce the numerical cost of the
offline phase, we exploit symmetries in the control problems. Furthermore, in
order to ensure optimality of the solutions, we include an additional online
optimization step, which is considerably cheaper than the original
multi-objective optimization problem. We test our framework on a car
maneuvering problem where safety and speed are the objectives. The
multi-objective framework allows for online adaptations of the desired
objective. Alternatively, an automatic scalarizing procedure yields very
efficient feedback controls. Our results show that the method is capable of
designing driving strategies that deal better with uncertainties in the initial
conditions, which translates into potentially safer and faster driving
strategies.}},
  author       = {{Hernández Castellanos, Carlos Ignacio and Ober-Blöbaum, Sina and Peitz, Sebastian}},
  journal      = {{International Journal of Robust and Nonlinear Control}},
  pages        = {{7593--7618}},
  title        = {{{Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty}}},
  doi          = {{10.1002/rnc.5197}},
  volume       = {{30(17)}},
  year         = {{2020}},
}

@article{29398,
  author       = {{Hernández Castellanos, C. I. O. and Schütze, G. and Sun, J.-Q. and Ober-Blöbaum, Sina and Morales-Luna, G.}},
  journal      = {{Mathematics}},
  title        = {{{Numerical computation of lightly multi-objective robust optimal solutions by means of generalized cell mapping}}},
  volume       = {{8(11):1959}},
  year         = {{2020}},
}

@inproceedings{29422,
  author       = {{Lishkova, Y. and Ober-Blöbaum, Sina and Cannon, M. and Leyendecker, S.}},
  booktitle    = {{Accepted for publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe}},
  title        = {{{A multirate variational approach to simulation and optimal control for flexible spacecraft}}},
  year         = {{2020}},
}

@inproceedings{29423,
  author       = {{Faulwasser, T. and Flaßkamp, K. and Ober-Blöbaum, Sina and Worthmann, K. }},
  booktitle    = {{24th International Symposium on Mathematical Theory of Networks and Systems}},
  title        = {{{A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems}}},
  year         = {{2020}},
}

@inproceedings{29424,
  author       = {{Cresson, J.  and Jiménez, F. and Ober-Blöbaum, Sina}},
  booktitle    = {{24th International Symposium on Mathematical Theory of Networks and Systems}},
  title        = {{{Modelling of the convection-diffusion equation through fractional restricted calculus of variations}}},
  year         = {{2020}},
}

@article{29545,
  author       = {{Jean, Frédéric and Maslovskaya, Sofya and Zelenko, Igor}},
  issn         = {{0046-5755}},
  journal      = {{Geometriae Dedicata}},
  keywords     = {{Geometry and Topology}},
  number       = {{1}},
  pages        = {{295--314}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry}}},
  doi          = {{10.1007/s10711-020-00581-z}},
  volume       = {{213}},
  year         = {{2020}},
}

@inproceedings{29546,
  author       = {{Maslovskaya, Sofya and Caillau, Jean-Baptiste and Djema, Walid and Giraldi, Laetitia and Jean-Luc, Jean-Luc and Pomet, Jean-Baptiste}},
  title        = {{{The turnpike property in maximization of microbial metabolite production}}},
  year         = {{2020}},
}

@inbook{29413,
  author       = {{Flaßkamp, K. and Ober-Blöbaum, Sina and Peitz, S. }},
  booktitle    = {{Advances in Dynamics, Optimization and Computation}},
  editor       = {{Junge, Oliver and Schütze, Oliver and Froyland, Gary and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}},
  pages        = {{209--237}},
  publisher    = {{Springer International Publishing}},
  title        = {{{Symmetry in optimal control: A multiobjective model predictive control approach}}},
  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}},
}

@article{16712,
  abstract     = {{We investigate self-adjoint matrices A∈Rn,n with respect to their equivariance properties. We show in particular that a matrix is self-adjoint if and only if it is equivariant with respect to the action of a group Γ2(A)⊂O(n) which is isomorphic to ⊗nk=1Z2. If the self-adjoint matrix possesses multiple eigenvalues – this may, for instance, be induced by symmetry properties of an underlying dynamical system – then A is even equivariant with respect to the action of a group Γ(A)≃∏ki=1O(mi) where m1,…,mk are the multiplicities of the eigenvalues λ1,…,λk of A. We discuss implications of this result for equivariant bifurcation problems, and we briefly address further applications for the Procrustes problem, graph symmetries and Taylor expansions.}},
  author       = {{Dellnitz, Michael and Gebken, Bennet and Gerlach, Raphael and Klus, Stefan}},
  issn         = {{1468-9367}},
  journal      = {{Dynamical Systems}},
  number       = {{2}},
  pages        = {{197--215}},
  title        = {{{On the equivariance properties of self-adjoint matrices}}},
  doi          = {{10.1080/14689367.2019.1661355}},
  volume       = {{35}},
  year         = {{2020}},
}

@article{45954,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>$L^2$ norm error estimates of semi- and full discretizations of wave equations with dynamic boundary conditions, using bulk–surface finite elements and Runge–Kutta methods, are studied. The analysis rests on an abstract formulation and error estimates, via energy techniques, within this abstract setting. Four prototypical linear wave equations with dynamic boundary conditions are analysed, which fit into the abstract framework. For problems with velocity terms or with acoustic boundary conditions we prove surprising results: for such problems the spatial convergence order is shown to be less than 2. These can also be observed in the presented numerical experiments.</jats:p>}},
  author       = {{Hipp, David and Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{1}},
  pages        = {{638--728}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates}}},
  doi          = {{10.1093/imanum/drz073}},
  volume       = {{41}},
  year         = {{2020}},
}

@article{45953,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>$L^2$ norm error estimates of semi- and full discretizations of wave equations with dynamic boundary conditions, using bulk–surface finite elements and Runge–Kutta methods, are studied. The analysis rests on an abstract formulation and error estimates, via energy techniques, within this abstract setting. Four prototypical linear wave equations with dynamic boundary conditions are analysed, which fit into the abstract framework. For problems with velocity terms or with acoustic boundary conditions we prove surprising results: for such problems the spatial convergence order is shown to be less than 2. These can also be observed in the presented numerical experiments.</jats:p>}},
  author       = {{Hipp, David and Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{1}},
  pages        = {{638--728}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates}}},
  doi          = {{10.1093/imanum/drz073}},
  volume       = {{41}},
  year         = {{2020}},
}

@article{45955,
  author       = {{Akrivis, Georgios and Feischl, Michael and Kovács, Balázs and Lubich, Christian}},
  issn         = {{0025-5718}},
  journal      = {{Mathematics of Computation}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Algebra and Number Theory}},
  number       = {{329}},
  pages        = {{995--1038}},
  publisher    = {{American Mathematical Society (AMS)}},
  title        = {{{Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation}}},
  doi          = {{10.1090/mcom/3597}},
  volume       = {{90}},
  year         = {{2020}},
}

@article{45952,
  author       = {{Kovács, Balázs and Li, Buyang and Lubich, Christian}},
  issn         = {{1463-9963}},
  journal      = {{Interfaces and Free Boundaries}},
  keywords     = {{Applied Mathematics}},
  number       = {{4}},
  pages        = {{443--464}},
  publisher    = {{European Mathematical Society - EMS - Publishing House GmbH}},
  title        = {{{A convergent algorithm for forced mean curvature flow driven by diffusion on the surface}}},
  doi          = {{10.4171/ifb/446}},
  volume       = {{22}},
  year         = {{2020}},
}

@article{55288,
  author       = {{Baier, St. and Technau, Marc}},
  journal      = {{J. Théor. Nombres Bordx.}},
  number       = {{2}},
  pages        = {{719–760}},
  title        = {{{On the distribution of αp modulo one in imaginary quadratic number fields with class number one}}},
  doi          = {{10.5802/jtnb.1141}},
  volume       = {{32}},
  year         = {{2020}},
}

@article{55286,
  author       = {{Technau, Marc}},
  journal      = {{J. Number Theory}},
  pages        = {{148–167}},
  title        = {{{Modular hyperbolas and Beatty sequences}}},
  doi          = {{10.1016/j.jnt.2019.07.022}},
  volume       = {{208}},
  year         = {{2020}},
}

@article{55287,
  author       = {{Shparlinski, I. E. and Technau, Marc}},
  journal      = {{Funct. Approximatio, Comment. Math.}},
  number       = {{1}},
  pages        = {{113–124}},
  title        = {{{Kloosterman sums with twice-differentiable functions}}},
  doi          = {{10.7169/facm/1845}},
  volume       = {{63}},
  year         = {{2020}},
}

@article{55283,
  author       = {{Barth, D. and Beck, M. and Dose, T. and Glaßer, Ch. and Michler, L. and Technau, Marc}},
  journal      = {{Theoretical Computer Science}},
  pages        = {{11–35}},
  title        = {{{Emptiness problems for integer circuits}}},
  doi          = {{10.1016/j.tcs.2020.03.023}},
  volume       = {{824-825}},
  year         = {{2020}},
}

@article{34842,
  abstract     = {{Let D<0 be a fundamental discriminant and denote by E(D) the exponent of the ideal class group Cl(D) of K=ℚ(√D). Under the assumption that no Siegel zeros exist we compute all such D with E(D) dividing 8. We compute all D with |D| ≤ 3.1⋅10²⁰ such that E(D) ≤ 8.}},
  author       = {{Elsenhans, Andreas-Stephan and Klüners, Jürgen and Nicolae, Florin}},
  issn         = {{0065-1036}},
  journal      = {{Acta Arithmetica}},
  keywords     = {{Algebra and Number Theory}},
  number       = {{3}},
  pages        = {{217--233}},
  publisher    = {{Institute of Mathematics, Polish Academy of Sciences}},
  title        = {{{Imaginary quadratic number fields with class groups of small exponent}}},
  doi          = {{10.4064/aa180220-20-3}},
  volume       = {{193}},
  year         = {{2020}},
}

@article{16710,
  abstract     = {{In this work we present a set-oriented path following method for the computation of relative global
attractors of parameter-dependent dynamical systems. We start with an initial approximation of the
relative global attractor for a fixed parameter λ0 computed by a set-oriented subdivision method.
By using previously obtained approximations of the parameter-dependent relative global attractor
we can track it with respect to a one-dimensional parameter λ > λ0 without restarting the whole
subdivision procedure. We illustrate the feasibility of the set-oriented path following method by
exploring the dynamics in low-dimensional models for shear flows during the transition to turbulence
and of large-scale atmospheric regime changes .
}},
  author       = {{Gerlach, Raphael and Ziessler, Adrian and Eckhardt, Bruno and Dellnitz, Michael}},
  issn         = {{1536-0040}},
  journal      = {{SIAM Journal on Applied Dynamical Systems}},
  pages        = {{705--723}},
  title        = {{{A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors}}},
  doi          = {{10.1137/19m1247139}},
  year         = {{2020}},
}