Learning structural uncertainties of nonlinear systems with RBF neural networks via persistently exciting control

This work presents a scheme for learning, online, the actual nonlinearities of systems in canonical form. The proposed architecture comprises of an on-line Radial Basis Function (RBF) neural network identifier and a controller, with the signals issued by the latter guaranteeing the satisfaction of a Persistency of Excitation (PE) condition for the RBF regressors employed. As a consequence, the neural network weight estimates are proven to converge to small neighborhoods of their true values; thus succeeding learning the actual system nonlinearities with quality guarantees. Key characteristic is the isolation between identifier and controller design, increasing the robustness level of the proposed on-line learning scheme. Finally, a simulation study is provided to demonstrate its effectiveness.