On the Choice of the Scheduling Variables for Dynamic Local Model Networks with Local Regularized FIR Models

The objective of system identification is to derive models from input/output data. To extend advancements in regularization techniques for linear finite impulse response (FIR) models to the nonlinear domain, we employ local model networks (LMNs) with locally regularized FIR models to identify nonlinear processes. The training of the LMN is performed using the local linear model tree (LOLIMOT) algorithm, resulting in both the partitioning of the model space and the estimation of the corresponding linear local models for each region. One key advantage of this algorithm lies in its ability to create separate input spaces for the linear models (x-space) and the validity functions (z-space) comprising the partitioning. While the most straightforward choice (x-space = z-space) results in an extremely high-dimensional z-space for local FIR models, we ad-dress this drawback by proposing different z-spaces spanned by the input spaces of autoregressive with exogenous inputs (ARX) models or Laguerre filter models, respectively. The theoretical capabilities for the proposed z-spaces are characterized. The superiority in terms of computation time, as well as comparable performance for Laguerre z-spaces and FIR z-spaces, is demon-strated through numerical examples. Additionally, the limitations for the utilization of ARX z-spaces are highlighted. Finally, all z-spaces have been evaluated on real-world data of a Wiener-Hammerstein benchmark. The FIR and Laguerre z- space showed comparable performance, while the ARX z-space performed worse.