Globally Neural Network Control of Nonlinear Time-Delay Systems via Static Gain Function

In this article, the globally adaptive neural network (NN) control problem is addressed for a class of nonlinear systems with mismatched uncertainties and unknown time-varying delays through a static gain function-based algorithm. The combination of the Lyapunov-Krasovskii functional (LKF), the static gain function-based backstepping technique and the radial basis function NN (RBF NN) approximation approach eliminates the effects of unknown time-varying delays and unknown nonlinearities. The additional terms generated by the derivative of LKF are divided into two parts, one part is dealt by virtual control laws and the other part is suppressed with static gain functions. Specifically, a smooth enough switching function is constructed, which ensures the global stability of the closed-loop system signals. Finally, the performance of the globally adaptive NN control scheme is revealed by simulation results.