Reproducing Kernel Hilbert Space Approach for the Online Update of Radial Bases in Neuro-Adaptive Control

Classical work in model reference adaptive control for uncertain nonlinear dynamical systems with a radial basis function (RBF) neural network adaptive element does not guarantee that the network weights stay bounded in a compact neighborhood of the ideal weights when the system signals are not persistently exciting (PE). Recent work has shown, however, that an adaptive controller using specifically recorded data concurrently with instantaneous data guarantees boundedness without PE signals. However, the work assumes fixed RBF network centers, which requires domain knowledge of the uncertainty. Motivated by reproducing kernel Hilbert space theory, we propose an online algorithm for updating the RBF centers to remove the assumption. In addition to proving boundedness of the resulting neuro-adaptive controller, a connection is made between PE signals and kernel methods. Simulation results show improved performance.