Real-time neural identification using a recurrent wavelet first-order neural network of a chaotic system implemented in an FPAA

Recurrent neural networks use sequential or time series data. These algorithms can be used in temporal or ordinal tasks, such as speech recognition, image captioning, and forecasting, among many others. This study introduces a novel approach to the real-time identification of chaotic trajectories using a Recurrent Wavelet First-Order Artificial Neural Network (RWFONN) in conjunction with a Field-Programmable Analog Array (FPAA). The FPAA physically implements the chaotic dynamics of a third-order Jerky equation system with reconfigurable analog electronic components through its voltage output. The trajectory acquisition of the voltage signals is carried out by a dSPACE 1104 board connected to MATLAB & Simulink and Control Desk, which serves as real-time identification data for the RWFONN. The first-order artificial network implements a Morlet wavelet activation function for the online training. It has the particularity to work without the need for multiple epoch training, validation, or dividing the data into batches. Instead, it validates the process by the filtered and mean square errors, affirming the RWFONN's precision in identifying and reproducing the chaotic behavior of the FPAA-modeled system. This breakthrough in real-time identification holds promise for applications demanding dynamic and unpredictable behaviors, such as random number generators, neural controllers, and cryptographic systems.