Input-independent, optimal interpolatory model reduction: Moving from linear to nonlinear dynamics

16 June 2016
Prof. Serkan Gugercin

For linear dynamical systems, model reduction has achieved great success. In the case of linear dynamics,  we know how to construct, at a modest cost, (locally) optimalinput-independent reduced models; that is, reduced models that are uniformly good over all inputs having bounded energy. In addition, in some cases we can achieve this goal using only input/output data without a priori knowledge of internal  dynamics.  Even though model reduction has been successfully and effectively applied to nonlinear dynamical systems as well, in this setting,  bot the reduction process and the reduced models are input dependent and the high fidelity of the resulting approximation is generically restricted to the training input/data. In this talk, we will offer remedies to this situation.

First, we will  review  model reduction for linear systems by using rational interpolation as the underlying framework. The concept of transfer function will prove fundamental in this setting. Then, we will show how rational interpolation and transfer function concepts can be extended to nonlinear dynamics, specifically to bilinear systems and quadratic-in-state systems, allowing us to construct input-independent reduced models in this setting as well. Several numerical examples will be illustrated to support the discussion.
  • Computational Mathematics and Applications Seminar