A reproducing Kernel Hilbert Space approach for the online update of Radial Bases in neuro-adaptive control

Classical gradient based adaptive laws in model reference adaptive control for uncertain nonlinear dynamical systems with a Radial Basis Function (RBF) neural networks adaptive element do not guarantee that the network weights stay bounded in a compact neighborhood of the ideal weights without Persistently Exciting (PE) system signals or a-priori known bounds on ideal weights. Recent work has shown, however, that an adaptive controller using specifically recorded data concurrently with instantaneous data can guarantee such boundedness without requiring PE signals. However, in this work, the assumption has been that the RBF network centers are fixed, which requires some domain knowledge of the uncertainty. We employ a Reproducing Kernel Hilbert Space theory motivated online algorithm for updating the RBF centers to remove this assumption. Along with showing the boundedness of the resulting neuro-adaptive controller, a connection is also made between PE signals and kernel methods. Simulation results show improved performance.