Adaptive neural network control of nonlinear systems with unknown time delays

In this paper, adaptive neural control is presented for a class of strict-feedback nonlinear systems with unknown time delays. Using appropriate Lyapunov-Krasovskii functionals, the uncertainties of varying unknown time delays are compensated for such that iterative backstepping design can be carried out. In addition, controller singularity problems are solved by using the integral Lyapunov function and employing practical robust neural network control. The feasibility of neural network approximation of unknown system functions is guaranteed by defining practical compact sets. It is proved that the proposed systematic backstepping design method is able to guarantee semi-global uniformly ultimately boundedness (SGUUB) of all the signals in the closed-loop system and the tracking error is proven to converge to a small neighborhood of the origin.