Robust Adaptive Backstepping Control of a Nonlinear System with Uncertainty, Disturbance and Unknown Time Delay

In this paper, robust adaptive control is presented for a class of nonlinear systems in strict feedback form with uncertain time delay. It is assumed that time delay is not known, thus terms having delays must not appear in adaptation and control laws. By using the Lyapunov-Krasovskii functional, terms having time delay are deleted from adaptation and control laws. The adaptive backstepping method is used to design a controller and it is shown that this controller guarantees global uniform asymptotic stability of the system. A controller is robust against uncertain time delay and bounded disturbances, which enter the system. Two simulation results are provided to show the effectiveness of the proposed approach.