Speaker
Description
We develop the theoretical framework for extending the quadrature based balanced truncation (QuadBT) method to linear systems with quadratic outputs (LQO). QuadBT which was originally designed for data-driven balanced truncation of standard linear systems with linear outputs only. We show that by sampling the extended impulse responses (kernels) and their derivatives (in the time domain) or the corresponding transfer functions (in the frequency domain), we can construct a reduced order model that mimics the approximation quality of intrusive balanced truncation. At its core, the method can be interpreted as an implicit sampling of the Gramians of the system using input-output observations. We demonstrate a proof of concept for the proposed framework on an example using numerically evaluated data. We also briefly discuss the extension of the QuadBT method for the more involved quadratic-bilinear (QB) system case.