Stable nonlinear adaptive control with growing radial basis function networks

Abstract

An adaptive control technique, using dynamic structure Gaussian radial basis function neural networks, that grow in time based on the location of the system's state in space, is presented for the affine class of nonlinear systems having unknown or partially known dynamics. The method results in a network that is ‘economic’ in terms of network size, for cases where the state spans only a small subset of state-space, by utilizing less basis functions than would have been the case if basis functions were centred on discrete locations covering the whole, relevant region of state-space. Additionally, the system is augmented with sliding control so as to ensure global stability if and when the state moves outside the region of state-space spanned by the basis functions, and to ensure robustness to disturbances that arise due to the network inherent approximation errors.