Adaptive output tracking control for a class of high-order nonlinear systems with time-delay

For time-delay and parameter uncertainties in high-order nonlinear systems, a problem of robust adaptive output tracking is investigated for the system. Applying the backstepping recursive method, a robust adaptive output tracking controller is designed to achieve robust control over a class of high-order nonlinear system with parameter uncertainties and time-delay. According to Lyapunov stability theory, Barbalat lemma and Gronwall inequality, it is proved that the designed state feedback controller not only guarantees the state of systems is uniformly bounded, but also ensures the tracking error of the systems converges to a small neighborhood. Finally, for this system, an example of simple pendulum that in the state of the hydraulic is simulated by using the MATLAB, and the simulation results further show that the designed state feedback controller has good tracking performance.