L1 Adaptive Output-Feedback Controller for Non-Strictly-Positive-Real Reference Systems: Missile Longitudinal Autopilot Design

This paper presents an extension of the L-1 adaptive output-feed back controller to systems of unknown relative degree in the presence of time-varying uncertainties without restricting the rate or their variation. As compared with earlier results in this direction, a new piecewise continuous adaptive law is introduced, along with the low-pass-filtered control signal that allows for achieving arbitrarily close tracking of the input and the output signals of the reference system, the transfer function or which is not required to be strictly positive real. Stability of this reference system is proved using a small-gain-type argument. The performance bounds between the closed-loop reference system and the closed-loop L-1 adaptive system can be rendered arbitrarily small by reducing the step size of integration. Missile longitudinal autopilot design is used as an example to illustrate the theoretical results.