Theoretically Verifiable Stability Margins for an Adaptive Controller

†† † ‡ § This paper seeks to provide the beginnings of a theoretically motivated V&V technique for adaptive controllers in the context of controlling uncertain flight vehicle dynamics. Using a Reduced Linear Asymptotic System (RLAS), which characterizes the asymptotic behavior of an adaptive system, a systematic approach is proposed for deriving the stability margins of an adaptive flight control system (AFCS). Robustness properties of the AFCS in the presence of input disturbances and unmodeled dynamics along with robustness margins are derived. Methods for tuning the free adaptive system parameters such as Γ are presented, which may be needed to satisfy the desired performance criteria. Making use of the fact that the RLAS is a linear time invariant system, optimization procedures based on output feedback and Linear Matrix Inequalities are proposed for tuning such free parameters. The approach is validated using simulations of a nonlinear 6 DoF aircraft model with actuator constraints.