Steepest descent algorithms for neural network controllers and filters

A number of steepest descent algorithms have been developed for adapting discrete-time dynamical systems, including the backpropagation through time and recursive backpropagation algorithms. In this paper, a tutorial on the use of these algorithms for adapting neural network controllers and filters is presented. In order to effectively compare and contrast the algorithms, a unified framework for the algorithms is developed. This framework is based upon a standard representation of a discrete-time dynamical system. Using this framework, the computational and storage requirements of the algorithms are derived. These requirements are used to select the appropriate algorithm for training a neural network controller or filter. Finally, to illustrate the usefulness of the techniques presented in this paper, a neural network control example and a neural network filtering example are presented.