In the first approach, all the states are assumed to be available; a neuro-adaptive state-feedback backstepping control is designed.

In the second approach it is assumed that the system states are not available for measurement. Therefore, an observer on K-filters is designed to estimate the immeasurable states.

In two methods, the upper bound of uncertainties is not required to be known in advance. By using NN through an adaptation mechanism, this upper bound is approximated.

One of the advantages of the proposed algorithms is that, the common strict positive real (SPR) condition is eliminated during the design procedure.

The Nussbaum-gain technique is effectively employed to design two adaptive controllers for SISO nonlinear systems.