Modelling non-linear control systems using the discrete Urysohn operator

TL;DR

This paper presents a novel method for modeling non-linear control systems using a discrete Urysohn operator, offering an efficient, real-time identification technique with demonstrated effectiveness on mechanical and real-world systems.

Contribution

It introduces a multiple-input discrete Urysohn operator and an iterative identification method that finds a unique minimum-norm solution for non-linear system modeling.

Findings

Effective modeling of non-linear systems demonstrated

Real-time identification is feasible with the proposed method

Applicable to complex real-world dynamic objects

Abstract

This paper introduces a multiple-input discrete Urysohn operator for modelling non-linear control systems and a technique of its identification by processing the observed input and output signals. It is shown that, due to the nature of the discrete Urysohn operator, the identification problem always has an infinity of solutions, which exactly convert the inputs to the output. The suggested iterative identification procedure, however, leads to a unique solution with the minimum norm, requires only few arithmetic operations with the parameter values and is applicable to a real-time identification, running concurrently with the data reading. The efficiency of the proposed modelling and identification approaches is demonstrated using an example of a non-linear mechanical system, which is represented by a differential equation, and an example of a complex real-world dynamic object.