Non-Convex Projected Nlms Algorithm for Adaptive Nonlinear Prediction

Prediction of nonlinear dynamic process remains a challenging and active research topic. In this paper, adaptive nonlinear prediction based on a Hammerstein-modeling approach is investigated. Motivated by the desire to represent the best fit to the nonlinear dynamical plant with the Hammerstein model, the prediction problem is first formulated as an optimization problem, which is essentially non-convex due to nonlinear structural characteristics of the Hammerstein model. Then, a projected normalized least-mean-square (P-NLMS) algorithm is developed for solving this non-convex optimization problem. The P-NLMS algorithm consists of two successive steps, i.e., adaptation and projection, where the adaptation step is based on the NLMS algorithm followed by an Euclidean projection onto the non-convex feasible region, and they respectively are use to update and refine the model parameters over time. Theoretical analysis shows that the proposed P-NLMS algorithm, compared with the existing algorithms, enjoys lower mean-squared-error and mean-square deviation. Several experiments further demonstrate that the P-NLMS algorithm has higher precision and better stability for the prediction of nonlinear dynamic process