Further Results on Model Reference Adaptive Control in the Presence of Actuator and Unmodeled Dynamics

In model reference adaptive control of uncertain dynamical systems, the presence of actuator and unmodeled dynamics are unavoidable. Our previous work focused on an adaptive control architecture for this problem and showed two sufficient stability conditions. In particular, the first condition captured the tradeoff between system uncertainties and actuator dynamics (related to the quadratic stability of a matrix) and the second condition captured the effect of unmodeled dynamics (related to the positive-definiteness of another matrix). This paper now proposes a robustifying term in this adaptive control architecture. Specifically, we show that this term results in an added nonnegative matrix in the second stability condition, where this can allow for a relaxed stability condition. Numerical examples are provided to demonstrate the efficacy of the proposed robustifying term on a coupled mechanical system.