Data driven discrete-time parsimonious identification of a nonlinear state-space model for a weakly nonlinear system with short data record

TL;DR

This paper presents a new methodology for identifying a parsimonious nonlinear state-space model for weakly nonlinear systems using short data records, employing polynomial-based initialization and tensor decomposition techniques.

Contribution

It introduces a novel approach combining polynomial initialization and tensor decomposition for efficient NLSS model identification from limited data.

Findings

Effective identification of NLSS models with short data records

Successful decoupling of multivariate polynomial representations

Experimental validation on cascaded water-benchmark system

Abstract

Many real world systems exhibit a quasi linear or weakly nonlinear behavior during normal operation, and a hard saturation effect for high peaks of the input signal. In this paper, a methodology to identify a parsimonious discrete-time nonlinear state space model (NLSS) for the nonlinear dynamical system with relatively short data record is proposed. The capability of the NLSS model structure is demonstrated by introducing two different initialisation schemes, one of them using multivariate polynomials. In addition, a method using first-order information of the multivariate polynomials and tensor decomposition is employed to obtain the parsimonious decoupled representation of the set of multivariate real polynomials estimated during the identification of NLSS model. Finally, the experimental verification of the model structure is done on the cascaded water-benchmark identification problem.