This paper introduces a multiple-input discrete Urysohn operator for modelling nonlinear control systems and a technique of its identification by processing the observed input and output signals. It is shown that 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. It is also shown that, depending on the input signal ranges, the discrete Urysohn operator can be identified partially and used in such form, which makes this dynamic model uniquely different to many others. 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.

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The block-oriented models are usually based on linear dynamic and non-linear static blocks that are connected in various sequential/parallel ways. Some particular configurations of the involved blocks result in the well-known Hammerstein, Wiener, Hammerstein-Wiener and generalised Hammerstein models. The Urysohn model is a lesser-known model; it is represented by a single non-linear dynamic block and can be approximated by a number of parallel Hammerstein blocks. In this paper, it is shown that any block-oriented model can be adequately replaced by a single Urysohn block followed by a single static non-linear block. Furthermore, a method of the so-called non-parametric identification of such object is introduced.

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