  This paper deals with the tracking control problem for a class of unknown
pure feedback system with pure state constraints on the state variables and
unknown time-varying bounded disturbances. An adaptive controller is presented
for such systems for the very first time. The controller is designed using the
backstepping method. While designing it, Barrier Lyapunov Functions is used so
that the state variables do not contravene its constraints. In order to cope
with the unknown dynamics of the system, an online approximator is designed
using a neural network with a novel adaptive law for its weight update. In the
stability analysis of the system, the time derivative of Lyapunov function
involves known virtual control coefficient with unknown direction and to deal
with such problem Nussbaum gain is used to design the control law. Furthermore,
to make the controller robust and computationally inexpensive, a novel
disturbance observer is designed to estimate the disturbance along with neural
network approximation error and the time derivative of virtual control input.
The effectiveness of the proposed approach is demonstrated through a simulation
study on the third-order nonlinear system.
