Key Words: Artificial neural network; approximation; Laguerre functions.
Abstract. The present article examines a well-known procedure used in various scientific fields – approximation. Specifically, it analyzes the application of Laguerre orthonormal functions in the approximation of transient and impulse responses of dynamic systems. Particular attention is given to the challenges associated with using these functions in the context of model predictive control (MPC) synthesis. These challenges include determining the scaling factor, the number of orthonormal functions, and the calculation of decomposition coefficients, which create additional difficulties when modeling systems with parametric uncertainties. To overcome these challenges, the use of artificial neural networks (ANN) is proposed for the automatic generation of the decomposition coefficients of Laguerre functions. Instead of directly approximating the impulse responses of systems, which involves significant computational complexity, ANN is employed to predict the optimal decomposition coefficients, thereby reducing computational time and improving accuracy. As part of the study, simulations were conducted for the approximation of both low- and high-order systems with different levels of parametric uncertainty. The results demonstrate a significant improvement in approximation accuracy when using neural networks compared to standard coefficient computation methods. Graphical representations of the approximation results for different values of the scaling factor and the number of orthonormal functions are provided, analyzing their effects on approximation error. It has been established that, with proper training of neural networks, significant improvements in the approximation process can be achieved, making them suitable for implementation in real-time control systems. The proposed methodology extends the applicability of Laguerre functions in model predictive control and provides an efficient approach for handling systems with uncertainties.
