In a recent paper we presented the first adaptive control design for an ODE system with a possibly large actuator delay of unknown length. We achieved global stability under full state feedback. In this paper we generalize the design to the situation where, besides the unknown delay value, the ODE also has unknown parameters, and where trajectory tracking (rather than equilibrium regulation) is pursued.

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Stabilization of an unstable system with an unknown actuator delay of substantial length is an important problem that has never been attempted. We present a Lyapunovbased adaptive control design, prove its stability and regulation properties for the plant and actuator states, and present a simulation example inspired by the problem of control of pitch and flight path rates in the unstable X-29 aircraft.