A Subspace Technique for The Identification of Switched Affine Models

TL;DR

This paper introduces a subspace-based method for identifying switched affine models from noisy data, transforming the problem into a permutation and clustering task to improve accuracy and efficiency.

Contribution

It presents a novel subspace technique that converts the parameter estimation problem into a permutation and clustering problem, enhancing performance and reducing complexity.

Findings

Improved accuracy over existing methods

Lower computational complexity

Effective for arbitrarily shaped domain partitions

Abstract

The problem of estimating parameters of switched affine systems with noisy input-output observations is considered. The switched affine models is transformed into a switched linear one by removing its intersection subspace, which is estimated from observations. A subspace technique is proposed to exploit the observations' permutation structure, which transforms the problem of associating observations with subsystems into one of de-permutating a block diagonal matrix, referred as adjacency matrix. Then a normalized spectral clustering algorithm is presented to recover the block structure of adjacency matrix, from which each observation is related to a particular subsystem. With the labelled observations, parameters of the submodel are estimated via the total least squares (TLS) estimator. The proposed technique is applicable to switched affine systems with arbitrarily shaped domain partitions, and it offers significantly improved performance and lowered computation complexity than existing techniques.