Semi-Global Stabilization of Nonlinear Time-Delay Systems Based on Dynamic Gain Approach

This paper investigates the adaptive state-feedback control problem of a two-stage chemical reactor system. Firstly, by using a direct radial basis function neural network (RBF NN) approximation approach, the nonlinear terms are handled under much weaker conditions. Then, with the help of a novel dynamic gain-based backstepping technique and appropriate Lyapunov-Krasovskii functionals, a smooth controller with only one adaptive parameter is constructed, which successfully overcomes the obstacles generated by time delay, control coefficients and nonlinear restrictions. It is proven that the constructed controller can render the closed-loop system semi-globally uniformly ultimately bounded. Finally, the simulation results of the chemical reactor system are shown to demonstrate the effectiveness of the control scheme.