Neural Networks for Function Approximation in Nonlinear Control

Two neural-network architectures are compared with a classical spline interpolation technique for the approximation of functions useful in a nonlinear control system. A standard back-propagation feedforward neural network and a Cerebellar Model Articulation Controller (CMAC) neural network are presented, and their results are compared with a B-spline interpolation procedure that is updated using recursive least-squares parameter identification. Each method is able to accurately represent a one-dimensional test function. Trade-offs between size requirements, speed of operation, and speed of learing indicate that neural networks may be practical for identification and adaptation in a nonlinear control environment.