Data-driven Learning for Approximation of Nonlinear Functions with Stochastic Disturbances
Quang Minh Ta, Huu-Thiet Nguyen, Chien Chern Cheah · 2020
In this paper, a data-driven learning approach is proposed for approximation of nonlinear functions with stochastic disturbances. A neural network is built and trained so as to approximate nonlinear mappings whose measured outputs are perturbed by stochastic disturbances. In the proposed approach, an adaptive-based learning algorithm is employed to update the weights of the neural network. Mathematical formulation is developed with the consideration of the stochastic disturbances, and the stability of the system for functional approximation tasks is ensured, even in the presence of the stochastic disturbances. Simulations on the approximation of arbitrary functions with different nonlinearities are then performed to illustrate the effectiveness of the proposed data-driven learning approach.