Approximation of Dynamic Systems Using Deep Neural Networks and Laguerre Functions ^†

This article presents a hybrid approach that combines Laguerre orthonormal functions with deep neural networks (DNN) for effective approximation of impulse responses of dynamic systems. Attention is given to key limitations in approximation with Laguerre functions, such as the selection of the optimal scaling factor, the number of functions used, and computational complexity. By training compact DNNs that directly predict the decomposition coefficients, increased functionality is achieved, as well as greater flexibility and efficiency in the context of implementing MPC. The proposed architecture provides good scalability, robustness, and computational efficiency, making it applicable in tasks related to system approximation and identification under uncertainty and noise conditions.