Shrinkage Strategies for Structure Selection and Identification of Piecewise Affine Models

TL;DR

This paper introduces two regularization-based heuristics for structure selection and identification of PieceWise Affine models with exogenous inputs, enabling simultaneous estimation of model structure and parameters.

Contribution

The paper presents novel optimization heuristics that jointly determine the number of sub-models and their parameters for PWA models using a coordinate-descent approach.

Findings

Effective in identifying PWA model structures from over-parameterized models

Demonstrated success on benchmark examples

Outperforms traditional methods in structure refinement

Abstract

We propose two optimization-based heuristics for structure selection and identification of PieceWise Affine (PWA) models with exogenous inputs. The first method determines the number of affine sub-models assuming known model order of the sub-models, while the second approach estimates the model order for a given number of affine sub-models. Both approaches rely on the use of regularization-based shrinking strategies, that are exploited within a coordinate-descent algorithm. This allows us to estimate the structure of the PWA models along with its model parameters. Starting from an over-parameterized model, the key idea is to alternate between an identification step and structure refinement, based on the sparse estimates of the model parameters. The performance of the presented strategies is assessed over two benchmark examples.