Modelling of Non-linear Control Systems using the Discrete Urysohn Operator

This paper shows a practical way of modelling non-linear dynamic systems with one input using the discrete form of the integral operator of the Urysohn type. A new iterative procedure for the identification of the Uryshon operator is proposed. It represents a sequence of elementary computational steps providing iterative improvements for the Urysohn model using observable input-output data. The controllability of the system is not required. The method is applicable as a real time identification process. The main advantages of the suggested identification technique are simplicity (the procedure can be implemented in 13 lines of Matlab code) and accuracy. It can also be used for the identification of one input Hammerstein and linear systems, since the Urysohn model is the generic form of these models. The efficiency of the algorithm is demonstrated using one example of a non-linear mechanical system with precise and noisy input-output data.