On realizability on neural networks-based input-output models (Q2734545)

The design of controllers for unknown plants is a challenge, especially for nonlinear plants. In the case where one has experimental input-output data, the task is first to obtain a mathematical model of the system and then to design the controller. Here a nonlinear system identification technique is often used, namely NARMA-type models are often exploited. An unknown function is commonly chosen to be a feedforward neural network (NN). On the other hand the state-space representation in the form of discrete difference equations has been used for a long time. The paper shows that the typical NN-based NARMA-type model does not have such a state-space realization in general. Then a new subclass of NN-based models that can be easily realized in the classical state space form is suggested. But the problem is that the approximation capabilities of the special function corresponding to such a subclass of NN-based models has not yet been established theoretically. Instead only one simulation is presented for supporting the claim.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00026].