Robust nonlinear system identification using neural network models

We study the problem of identification for nonlinear systems in the presence of unknown driving noise, using both feedforward multilayer neural network and radial basis function network models. The difficulty associated with the Persistency of Excitation condition (inherent to the standard schemes in the neural identification literature) is circumvented here by a novel formulation and by using a new class of identification algorithms recently obtained in [1]. By embedding the original problem in one with noise-perturbed state measurements, we present a class of identifiers (under L₁ and L₂ cost criteria) which secure a good approximant for the system nonlinearity provided that some global optimization technique is used. For one special network structure, viz. the RBF network, we present a neural network version of and H^∞-based identification algorithm from [1], and show how, along with an appropriate choice of control input to enhance excitation, under both full-state-derivative information and noise-perturbed full-state information, it leads to satisfaction of a relevant persistency of excitation condition, and thereby to robust identification of the system nonlinearity.