# Mathematics Colloquia and Seminars

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### Model Reduction for Nonlinear Systems without Snapshots

**PDE and Applied Math Seminar**

Speaker: | Peter Benner, Max-Planck Institute, Magdeburg |

Location: | 1147 MSB |

Start time: | Tue, Feb 11 2014, 3:10PM |

We discuss Krylov-subspace based model reduction techniques for nonlinear control systems. Since reduction procedures of existent approaches like TPWL and POD methods require simulation of the original system to produce snapshots at different time instances and are therefore dependent on the chosen input function, models that are subject to variable excitations might not be sufficiently approximated. We will overcome this problem by generalizing Krylov-subspace methods known from linear systems to a more general class of bilinear and quadratic-bilinear systems, respectively. As has recently been shown, a lot of nonlinear dynamics can be represented by the latter systems. We will explain advantages and disadvantages of the different approaches and illustrate their behavior for several benchmark examples from the literature. This is joint work with Tobias Breiten (University of Graz, Austria).