Distributed Prediction via Adaptive Hammerstein Filter Over Networked Systems

The problem of distributed prediction for a nonlinear dynamical plant of interest based on the collections of a networked system is considered. The Hammerstein filter is used as a predictive model, and two types of adaptive distributed Hammerstein filters (dHFs) are proposed, in which the parameters are collaboratively estimated via a diffusion cooperative rule. The performances of the proposed dHFs in the mean and mean-square senses are analyzed. Moreover, considering the sparsity of the model parameter vector in some real applications, two sparse distributed Hammerstein filters (Sp-dHFs) are further developed. Finally, some numerical simulations are performed to show the effectiveness of the proposed dHFs and Sp-dHFs in parameter estimation and prediction. Results show that the performances of the proposed dHFs and Sp-dHFs are very close to that of the corresponding centralized Hammerstein filter, while significantly better than that of the noncooperative Hammerstein filter in accuracy and robustness to the failure of nodes. Besides, when the system parameter vectors are sparse, Sp-dHFs outperform dHFs and the degree of superiority increases as the level of sparsity increases.