complete automated structure discovery and parameter estimation for piecewise affine models with guaranteed convergence

This paper presents a novel, fully automated framework for the complete structure discovery and parameter estimation of piecewise affine (pwa) models. to the best of our knowledge, this is the first approach that simultaneously determines the number of submodels, their orders, parameter vectors, and polyhedral partitions from data, without any prior structural knowledge or the need for tuning parameters. the methodology integrates three key innovations: (1) automated submodel order selection via orthogonal least squares with an error-to-signal ratio test; (2) a clustering-based algorithm for determining the number of submodels and generating a robust initial labeled dataset; and (3) an iterative algorithm that integrates a novel self-labeling support vector machine (sl-svm) for estimating polyhedral partitions with a recursive least squares (rls) scheme for refining submodel parameters, both with guaranteed convergence. theoretical analysis demonstrates both computational efficiency and convergence properties, with the sl-svm algorithm significantly reducing complexity compared to standard svm. extensive simulations validate the framework's performance across multiple benchmark systems, achieving best fit rates exceeding 98% in scenarios of complete structural uncertainty. the approach consistently outperforms existing methods in accuracy while maintaining computational efficiency. furthermore, we demonstrate the method's applicability to nonlinear system identification through pwarx approximation, showcasing its versatility for practical engineering applications. the proposed framework represents a significant advancement in automated system identification, providing a comprehensive solution for black-box modeling of hybrid and nonlinear systems.