Multi-Dimensional Locally Generalizing Neural Networks for Real Time Control

Abstract

Based on the fast learning convergence properties of networks with local generalization (compared to multi-layered networks with global learning interference and possible multi-minima), this paper reviews three locally generalizing neural networks: Radial Basis Functions (RBF), B-Splines (BSPL), and Cerebellar Model Articulated Controller (CMAC). In specific, the learning performance of the CMAC network was evaluated using a non-linear time series with four inputs and two outputs, and compared to those using RBF (Chen, Billings (1991)) and B-Splines(Brown, Harris (1991)). In relation to real-time control tasks, either the plant derivative (or jacobian) or an approximated version of the jacobian is required if the controller is adjusted based on an instantaneous tracking error (instead of the control error). This way the controller becomes sensitive to the estimated plant jacobian. This paper also studies the ability of the CMAC network to approximate a plant made of multi-sinusoids, and estimate the plant jacobian based on the approximated plant model.