Adaptive controller design for a class of nonlinear time-delay systems with uncertainties

A robust adaptive controller is designed for a class of strict-feedback nonlinear time-delay systems with uncertainties. Using Lyapunov-Krasovskii functionals, the uncertainties of unknown time delays are compensated for. By introducing an appropriate even function, controller singularity problems are solved. It is shown that the proposed backstepping design procedure is able to guarantee global uniform ultimate boundedness of all the signals in the closed-loop system, the tracking error is proven to converge to a small neighborhood of the origin. A simulation example is provided to illustrate the validity of the proposed controller.