On Nonlinear System Invertibility and Learning Approaches by Neural Networks

In many system control application areas, neural networks are often used to learn the inverse of a given system in terms of the system output information. The study of system invertibility becomes necessary for design of control systems incorporated with neural networks. A class of nonlinear dynamic systems, such as robotic systems, has been investigated in finding a lower bound of the system relative orders. This study turns out a useful criterion for determining the least number of excitations to a neural network to be designed for learing the system inverse. It has also been investigated by many researchers that through learning, a three-layer neural network can implement a function of certain types within any error accuracy. In this paper, utilizing all previous results in considerations of the least number of excitations, function approximations and the least number of hiden processing elements, the design of neural network architectures and learning approaches are further studied. A supervised learning strategy used to train a neural network to be a functional block for controlling robotic systems are also explored and discussed.