Adaptive dynamic surface neural control of pure-feedback nonlinear time-delay systems

This paper is concerned with robust stabilization problem for a class of nonaffine pure-feedback systems with unknown time-delay functions and perturbed uncertainties. Novel continuous packaged functions are introduced in advance to remove unknown nonlinear terms deduced from perturbed uncertainties and unknown time-delay functions, which avoids the functions with control law to be approximated by radial basis function (RBF) neural networks. This technique combining implicit function theorem and mean value theorem overcomes the difficulty in controlling the nonaffine pure-feedback systems. Dynamic surface control (DSC) is used to avoid “the explosion of complexity” in the backstepping design. The unknown time-delay functions are compensated for using Lyapunov-Krasovskii functionals, RBF neural networks are employed to approximate desired virtual controls and desired practical control. Under the proposed adaptive neural DSC, the number of adaptive parameters required is reduced significantly, and semi-global uniform ultimate boundedness of all the signals in the closed-loop system is guaranteed. Simulation studies are given to demonstrate the effectiveness of the proposed scheme.