An Algorithm for System Identification of a Discrete-Time Polynomial System without Inputs

TL;DR

This paper introduces a subalgebraic algorithm for identifying the parameters of a discrete-time polynomial system without inputs, using time series data and algebraic techniques like SVD and polynomial factorization.

Contribution

It presents a novel algorithm for system identification that does not require input data, focusing on polynomial systems and employing algebraic methods.

Findings

Successfully estimates system parameters from time series data.

Uses singular value decomposition and polynomial factorizations effectively.

Provides an illustrative example demonstrating the algorithm's application.

Abstract

A subalgebraic approximation algorithm is proposed to estimate from a set of time series the parameters of the observer representation of a discrete-time polynomial system without inputs which can generate an approximation of the observed time series. A major step of the algorithm is to construct a set of generators for the polynomial function from the past outputs to the future outputs. For this singular value decompositions and polynomial factorizations are used. An example is provided.