An Lmi-based Hedging Approach to Model Reference Adaptive Control with Actuator Dynamics

Although model reference adaptive control 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, an 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 does not get affected due to the presence of actuator dynamics. Specifically, we first generalize the hedging approach to cover cases in which actuator output and is known and unknown. We next show the stability of the closed-loop dynamical system using tools from Lyapunov stability and linear matrix inequalities. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed linear matrix-inequalities-based hedging approach to model reference adaptive control.