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This paper introduces a multiple-input discrete Urysohn operator formodelling non-linear control systems and a technique of its identification byprocessing the observed input and output signals. It is shown that, due to thenature of the discrete Urysohn operator, the identification problem always hasan infinity of solutions, which exactly convert the inputs to the output. Thesuggested iterative identification procedure, however, leads to a uniquesolution with the minimum norm, requires only few arithmetic operations withthe parameter values and is applicable to a real-time identification, runningconcurrently with the data reading. The efficiency of the proposed modellingand identification approaches is demonstrated using an example of a non-linearmechanical system, which is represented by a differential equation, and anexample of a complex real-world dynamic object.

Modelling non-linear control systems using the discrete Urysohn operator