Delay-adaptive full-state predictor feedback for systems with unknown long actuator delay

Stabilization of unstable systems with actuator delay of substantial length and of completely unknown value is an important problem that has never been attempted. We present a Lyapunov-based adaptive control design that achieves global stability, without a requirement that the delay estimate be near the true delay value. We solve the problem by employing a framework where the actuator delay is represented as a transport PDE, by estimating the delay value as the reciprocal of the convection speed in the transport PDE, and by using full state predictor-based feedback.