Feedback Linearization Using a Minimized Structure Neural Network

For a class of single-input single-output continuous-time nonlinear systems, a three-layer neural network-based controller that feedback linearizes the system is presented. Control action is used to achieve tracking performance for a feedback linearizable but unknown nonlinear system. The control structure consists of a feedback linearization portion provided by two neural networks plus a robustifying portion that keeps the control magnitude bounded. This paper, in some sense, is the contribution of the work done in Yesildirek and Lewis,1995. It is shown that a new look at the weight update formulas makes it possible to obtain very simple network structures with only two neurons in their hidden layers, which results in a reduced number of controller equations without changing the corresponding stability results. This reduces network complexities and makes output tracking faster. It is shown that all the signals in the closed-loop system are uniformly ultimately bounded. No off-line learning phase is needed, Initialization of the network weights is straightforward. Copyright © 2002 IFAC