Practical adaptive neural control of nonlinear systems with unknown time delays

In this paper, practical adaptive neural control is presented for a class of nonlinear systems with unknown time delays in strict-feedback form. Using appropriate Lyapunov-Krasovskii functional, the uncertainties of unknown time delays are compensated for. Controller singularity problems are solved by employing practical neural network control based on decoupled backstepping design. It is proved that the proposed design method is able to guarantee semi-globally uniformly ultimate boundedness of all the signals in the closed-loop system and the tracking error is proven to converge to a small neighborhood of the origin. In addition, the residual set of each states in the closed-loop systems can be determined respectively.