Model reference adaptive control in the presence of high-order actuator dynamics

We recently proposed a linear matrix inequalities-based hedging approach to compute stability limits of adaptive controllers in the presence of first-order actuator dynamics. Specifically, our approach modifies the ideal reference model dynamics using the hedging method to allow correct adaptation, which is not affected by the presence of actuator dynamics, and then analyzes the stability of this modified reference model coupled with the first-order actuator dynamics using linear matrix inequalities - for computing the fundamental stability interplay between the bandwidth of actuator dynamics and the allowable system uncertainties. This paper generalizes this framework to high-order (linear time-invariant) actuator dynamics and discuss the distance between the uncertain dynamical system and the ideal (i.e., unmodified) reference model dynamics. An illustrative numerical example is provided to demonstrate the efficacy of the proposed approach in computing stability limits of adaptive controllers.