Adaptive Robust Tracking Control for First-Order Linear Systems with Input Delay and Lipschitz Nonlinear Disturbance

In this paper, an adaptive robust tracking controller is proposed for first-order linear systems with input delay, unknown plant parameters and Lipschitz nonlinear disturbance. The controller employs the predictor feedback to compensate for the effect of input delay, the robust feedback to deal with uncertainties, the model compensation for trajectory tracking, and projection-type adaptation laws are designed. By the stability analysis with a Lyapunov function in integral form, the closed-loop system is locally stable in the sense that the tracking error is bounded above by a known function which exponentially converges to a specified accuracy provided that the initial states and control parameters meet certain conditions. Furthermore, when the disturbance is reduced to a constant, the controller guarantees the semi-global stability that the tracking error asymptotically converges to zero. Simulation results demonstrate the effectiveness of the proposed controller.