This study addresses the proposition of neural network (NN) adaptive control for a class of nonlinear systems using fuzzy reasoning. In first step, an ideal control law is established based on feedback linearization technique and certainty equivalence. Then the NN system is introduced on line to approximate this ideal control law. The parameters of the NN system are on-line adapted and changed according to the gradient descent law, which will be approximated in part by a fuzzy inference system. In other words, instead of using the popular back propagation technique. we use an on-line simple fuzzy inference system to approximate part of the gradient descent resulting adaptation law

Keywords: Fuzzy inference reasoning, Neural network adaptive control, Certainty equivalence feedback linearization, Nonlinear instable system