Adaptive neural control for a class of nonlinearly parametric time-delay systems: first order case

In this paper, an adaptive neural controller for a class of first-order time-delay nonlinear systems with unknown nonlinearities is proposed. Based on WNN (wavelet neural network) online approximation model, a state-feedback adaptive controller is obtained by constructing an novel Integral-type Lyapunov-Krasovskii functional. The key assumption is that the time-delay term of the systems satisfies a certain inequality condition. The proposed method guarantees semi-global uniform ultimate boundedness for the adaptive closed-loop systems. An example is provided to illustrate the application of the approach.