Adaptive NN control for a class of strict-feedback nonlinear systems with time delays

In this paper, a novel adaptive NN control scheme is proposed for a class of uncertain single-input and single- output(SISO) nonlinear time-delay systems with the lower triangular form. RBF NNs are used to approximate unknown nonlinear functions, then the adaptive NN tracking controller is constructed by combining Lyapunov-Krasovskii functionals and the dynamic surface control(DSC) technique along with the minimal-learning-parameters(MLP) algorithm. The proposed controller guarantees uniform ultimate boundedness of all the signals in the closed-loop system, while the tracking error converges to a small neighborhood of the origin. An advantage of the proposed control scheme lies in that the number of adaptive parameters is reduced dramatically to one, both problems of “explosion of complexity” and “curse of dimension” are solved simultaneously.