Dynamic structure neural networks for stable adaptive control of nonlinear systems

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Abstract
An adaptive control technique, using dynamic structure Gaussian radial basis function neural networks, that grow in time according to 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 centered 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 and to the fact that for limiting the network size, a minimal number of basis functions are actually being used. Adaptation laws and sliding control gains that ensure system stability in a Lyapunov sense are presented, together with techniques for determining which basis functions are to form part of the network structure. The effectiveness of the method is demonstrated by experiment simulations.