Approximation of Fractional Order Dynamic Systems Using Elman, GRU and LSTM Neural Networks

Abstract

In the paper, authors explore the possibility of using the recurrent neural networks (RNN) - Elman, GRU and LSTM - for an approximation of the solution of the fractional-orders differential equations. The RNN network parameters are estimated via optimisation with the second order L-BFGS algorithm. It is done based on data from four systems: simple first and second fractional order LTI systems, a system of fractional-order point kinetics and heat exchange in the nuclear reactor core and complex nonlinear system. The obtained result shows that the studied RNNs are very promising as approximators of the fractional-order systems. On the other hand, these approximations may be easily implemented in real digital control platforms.