Adaptive backstepping control of uncertain linear systems under unknown actuator delay

Trajectory tracking of uncertain time-delay linear systems by output feedback control is of theoretical importance and practical value. In this paper, concentrating on a class of linear plants whose relative degree equals to system dimension, we develop a Lyapunov-based control scheme to achieve trajectory tracking despite some classic difficulties including unmeasurable system state, unknown plant parameters and unknown input time-delay. A comprehensive approach combining adaptive backstepping output feedback with prediction-based boundary control is employed in the design. The stability analysis exhibits the global boundedness of all closed-loop system signals and the tracking performance is also guaranteed.