Computing actuator bandwidth limits for model reference adaptive control

Although model reference adaptive control theory has been used in numerous applications to achieve system performance without excessive reliance on dynamical system models, the presence of actuator dynamics can seriously limit the stability and the achievable performance of adaptive controllers. In this paper, a linear matrix inequalities-based hedging approach is developed and evaluated for model reference adaptive control of uncertain dynamical systems in the presence of actuator dynamics. The hedging method modifies the ideal reference model dynamics in order to allow correct adaptation that is not affected by the presence of actuator dynamics. Specifically, we first generalise the hedging approach to cover a variety of cases in which actuator output and the control effectiveness matrix of the uncertain dynamical system are known and unknown. We then show the stability of the closed-loop dynamical system using Lyapunov-based stability analysis tools and propose a linear matrix inequality-based framework for the computation of the minimum allowable actuator bandwidth limits such that the closed-loop dynamical system remains stable. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.