Direct adaptive control with multi-grid networks

Approximation of an unknown function can be effectively implemented with neural networks. A function represented by measurements obtained in real time is modeled by a Gaussian Radial Basis Function (RBF) network. A network proposed R. Sanner and J.J.B. Slottine (see IEEE Trans. on Neural Networks, vol.3, no.6, 1992) for this goal is modified to reduce the number of neurons necessary to guarantee the desired approximation accuracy. The proposed network consists of a series of grids defined as sets of neurons located, in the nodes of lattices of increasing density, with consecutive grids including all the previous ones. The grids of low density are responsible for approximation of global features of a function, and the grids of higher density are responsible for approximation of the local function properties. reduction of the network size is due to adaptive network architecture. At the beginning, the network consists of only the lowest density grid and all its neurons are idle, i.e., they just express a possibility of the neuron existence at a given position. During learning, the idle neurons of a grid can be transformed into the active ones to suit the local accuracy requirements, and if this is not sufficient, the next (higher density) lattice of idle neurons is included into the network, thus enabling for higher-frequency contents to be modeled. The proposed design was applied to a tracking control problem for two second order plants. Experiments showed good performance of control with considerably reduced number of neurons, as compared to a single-layer solution of of Sanner and Slottine