On-line identification of non-linear systems using adaptive rbf-based neural networks

This paper extends the sequential learning algorithm strategy of two different types of adaptive radial basis function-based (RBF) neural networks, i.e. growing and pruning radial basis function (GAP-RBF) and minimal resource allocation network (MRAN) to cater for on-line identification of non-linear systems. The original sequential learning algorithm is based on the repetitive utilization of sequential input-output data in order to accomplish the training phase. Some interesting modifications have been proposed in the growing and pruning neurons criteria of the original GAP-RBF neural network to make the resulting modified GAP-RBF (MGAP-RBF) neural network suitable for on-line system identification applications. The Unscented Kalman Filter (UKF) has been proposed as a new learning algorithm to update the parameters of MRAN, GAP-RBF and MGAP-RBF neural networks. Moreover, to keep the resulting parameter estimation routines more sensitive to track any possible time-varying system dynamics, a variable forgetting factor strategy has been included in the UKF learning algorithm. The proposed identification algorithms have been tested on a nonisothermal continuous stirred tank reactor (CSTR) and the chaotic Mackey Glass time-series as two different benchmark problems. The resulting performances of the MRAN, GAP-RBF and the proposed MGAP-RBF neural networks being estimated with the extended Kalman filter (EKF) or the UKF learning algorithm have been evaluated for comparison purposes. Simulation results show the superiority of the proposed MGAP-RBF neural network estimated with the UKF learning algorithm.