Feedback linearization of unknown nonlinear systems using neural networks-an application to motor control

This paper presents a method to feedback linearize unknown nonlinear system by means of an adaptive scheme implemented by the use of neural networks. For a restricted class of systems, necessary conditions for teaching the feedback linearizing function to a multilayer neural network, trained by the generalized delta rule, are presented. In the proposed scheme, two neural networks are trained in three different stages. In the first stage, the nonlinear system is excited several times to teach the system inverse dynamics to a neural network. In the second stage, the system is again excited several times to train a second neural network with an estimation of the feedback linearizing function of the nonlinear system. After the two stages of training, the system is operated with the second neural network as feedback, its weights are adaptively adjusted to accommodate possible parameter variations in the nonlinear system. Some preliminary results are presented, showing the feedback linearization of a DC motor with a nonlinear load