A two-stage learning framework for piecewise affine system identification

This paper proposes a fully data-driven and end-to-end adaptive framework for the complete black-box identification of piecewise affine ARX (PWARX) systems, in which model structure discovery, submodel parameter estimation, recursive parameter fine-tuning, and explicit polyhedral partition identification are integrated into a unified two-stage learning architecture. In Stage 1, an unsupervised process determines the number and order of submodels, computes consistent initial submodel parameter estimates, and constructs a compact labeled training set. In Stage 2, a self-tuning semi-supervised support vector machine (STS3VM) iteratively learns the submodel classifiers, while adaptive-forgetting recursive least squares fine-tunes the submodel parameters. The learned decision rule is then converted into explicit polyhedral partitions, with stage-wise convergence guarantees. Extensive simulations demonstrate high accuracy, reproducibility, robustness under diverse noise conditions, and scalability.