Robust adaptive control of nonlinear systems with unknown time delays

In this work, robust adaptive control is presented for a class of parametric-strict-feedback nonlinear systems with unknown time delays. Using appropriate Lyapunov-Krasovskii functional, the uncertainties of unknown time delays are compensated for. Controller singularity problems are solved by employing practical robust control and regrouping unknown parameters. By using differentiable approximation, backstepping design can be carried out for a class of nonlinear systems in strict-feedback form. It is proved that the proposed systematic backstepping design method is able to guarantee global uniformly ultimately 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.