On Bilinear Time-Domain Identification and Reduction in the Loewner Framework

The Loewner framework (LF) in combination with Volterra series (VS) offers a non-intrusive approximation method that is capable of identifying bilinear models from time-domain measurements. This uses harmonic inputs which establish natural way for data acquisition. For the general class nonlinear problems VS representation, growing exponential approach allows derivation generalized kernels, namely, symmetric frequency response functions (GFRFs). In addition, homogeneity operator determines accuracy terms how many kernels are considered. weakly setup, only few needed to obtain good approximation. this direction, proposed adaptive scheme able improve estimations computationally nonzero kernels. Fourier transform associates these measurements derived GFRFs and LF makes connection system theory. linear case, so-called S-parameters transfer function by interpolating domain. goal extend identification case systems approximate other (by means Carleman bilinearizarion scheme). By contribution LF, considerable reduction achieved SVD. fitted has same McMillan degree as original system. Then, performance model improved augmenting special structure. nutshell, we learn reduced-dimension directly potentially large-scale simulated time done fitting first model, afterward, corresponding operator.