The problem of transforming a nonlinear system to a linear system has received much attention in the literature. The interest in linear systems originates from the fact that such systems have been widely studied and there is a rich theoretical background as well as sophisticated design tools for controller synthesis. The set up is: Given a continuous nonlinear system of the form
x=f(x) + g(x).u
y=h(x)
where x, y, and u represent the states, the ouputs, and the inputs, the objective is to transform the system using nonlinear feedback and a change of coordinates in the state-space to a linear system. If such a transformation is possible, the feedback linearizing law can be computed in closed form using the system data, f, g, and h, such that the nonlinear system behaves linearly from input to output locally around a point x0 in the state-space. If these functions are not known analytically but the feedback linearization law is known to exist, then it needs to be computed differently. In this thesis, different techniques are developed for learning the feedback linearization law employing multilayer feedforward networks and the generalized delta rule as a learning mechanism. For SISO systems, it is shown that for any subset of the neighborhood of x0, the feedback linearization law can be learned by such networks assuming the states of the system are measurable and γ, the relative degree of the system, is either equal to the system dimension or the nonlinear system is minimum-phase. Depending on the complexity of the system, several multilayer networks can be used to learn and to implement the nonlinear state feedback where each is activated depending on a specific situation. Each network is trained in an unsupervised mode. An appropriate linear reference model with relative degree of at least γ is used as a teacher such that after training, the closed loop system will behave approximately the same as the reference model. The input-output behavior of the nonlinear system is to match as close as possible the input-output behavior of the linear reference model after state feedback is applied to the nonlinear system. The state feedback can be implemented in two different modes: statically or dynamically. The advantage of the dynamic method is in its adaptive nature where the controller (network) parameters change on-line to compensate for slowly varying parameters in the nonlinear plant. A new method is introduced to discover the control law directly from the error between the system and the reference model outputs. The emphasis will be on continuous SISO systems, however, discrete-time systems as well as MIMO systems will be discussed briefly.