Krylov subspace methods for model reduction of MIMO quadratic-bilinear systems

Model order reduction for large-scale nonlinear dynamical systems has gained a lot of attention in the past ten years. Well-known simulation-based techniques like POD and TPWL are widely used, especially for the reduction of complex and strong nonlinear systems. Since these methods rely on expensive simulations for different training input signals, the reduced models are input dependent and might therefore yield moderate approximations when subjected to other excitation signals. In order to overcome this issue, popular linear system-theoretic reduction techniques like balanced truncation, Krylov subspace methods and H2 optimal approaches have been recently generalized and successfully applied to bilinear [1, 5] and quadratic-bilinear systems [2, 3, 4]. In this talk, we focus on MIMO quadratic-bilinear systems. First, the systems theory and transfer function concepts known from the SISO case are studied and extended to the MIMO case. Then, new block and tangential Krylov reduction methods for MIMO quadratic-bilinear systems will be reported, analyzed and their performance compared.      «

Model order reduction for large-scale nonlinear dynamical systems has gained a lot of attention in the past ten years. Well-known simulation-based techniques like POD and TPWL are widely used, especially for the reduction of complex and strong nonlinear systems. Since these methods rely on expensive simulations for different training input signals, the reduced models are input dependent and might therefore yield moderate approximations when subjected to other excitation signals. In order to over...     »