On Adaptive Control of Uncertain Dynamical Systems in the Presence of Actuator Dynamics and Amplitude Saturation Limits

In this paper, we propose a model reference adaptive control approach for uncertain dynamical systems in the presence of both actuator dynamics and actuator amplitude saturation limits. Specifically, we use a new expanded reference model including a deficit term between the ideal control signal and its saturated version. Closed-loop system stability of the proposed approach utilizing this expanded reference model is analyzed using linear matrix inequalities (LMIs) and Lyapunov theory, where the resulting stability conditions capture the interplay between the allowable actuator dynamics, actuator amplitude saturation limits, initial conditions, and the system uncertainties. An illustrative numerical example is further provided to demonstrate the efficacy of the proposed approach.