Modelling non-linear control systems using the discrete Urysohn operator

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.