A. Atinga, A. R. Várkonyi-Kóczy, J. Tar: Application of Abstract Rotations for Forecasting the Signals of Nonlinear Dynamic Systems. In IEEE 10th Jubilee International Conference on Computational Cybernetics and Cyber-Medical Systems (ICCC 2022) Proceedings. pp. 389-394, 2023. ISBN 978-1-6654-8177-9 link

Abstract: Occurrence of delayed signals is quite general in control technology. In most cases it appears as a problem that partly can be tackled by signal forecasting or prediction techniques. In certain applications it is intentionally applied for realizing a special kind of machine learning as e.g., in the Fixed Point Iteration-based adaptive controllers. To improve the efficiency of such adaptive controllers a special function was constructed in 2018. This function received two input columns of different sizes and computed a rotational operator acting in a space of augmented dimension so that it exactly rotated one of the augmented input vector to the other one. Later it was revealed that its good generalization property makes it possible to develop topologically very simple neural networks as soft computing-based dynamic model representations in which the activation function of each neuron makes abstract rotations. The idea of using such functions for the prediction of the signals produced by nonlinear dynamic systems naturally arose. To the best knowledge of the Authors this is the first time when such investigations are reported. The strongly dynamic signal of a van der Pol oscillator is predicted for a relatively short time interval by this nonlinear rotational method. The results of this prediction are compared with that of a simple prediction method that applies fitted linear combinations for transforming the input array into the output. The numerical simulations indicate that the suggested nonlinear method is considerably better (more precise) than the linear one. It seems to be expedient to make further investigations for dynamical systems of different order and noise sensitivity.