Computing stability limits for adaptive control laws with high-order actuator dynamics

Abstract

A challenge in the design of adaptive control laws for uncertain dynamical systems is to achieve system stability and a prescribed level of command following performance in the presence of actuator dynamics. It is well-known that if the actuator dynamics do not have sufficiently high bandwidth, their presence cannot be practically neglected in the design since they limit the achievable stability of adaptive control laws. In this paper, we consider the design of model reference adaptive control laws for uncertain dynamical systems in the presence of high-order actuator dynamics. Specifically, a linear matrix inequalities-based hedging approach is proposed, where this approach modifies the ideal reference model dynamics to allow for correct adaptation that is not affected by the presence of actuator dynamics. The stability of the modified reference model is then computed using linear matrix inequalities, which reveals the fundamental stability interplay between the parameters of the actuator dynamics and the allowable system uncertainties. In addition, we analyze the convergence properties of the modified reference model to the ideal reference model. The presented theoretical results are finally illustrated through a numerical example.