On Model Reference Adaptive Control for Uncertain Dynamical Systems with Unmodeled Dynamics

On model reference adaptive control for uncertain dynamical systems, it is well know that there exists a fundamental stability limit, where the closed-loop dynamical system subject to this class of control laws remains stable either if there does not exist significant unmodeled dynamics or the effect of system uncertainties is negligible. Specifically, this implies that model reference adaptive controllers cannot tolerate large system uncertainties even when unmodeled dynamics satisfy a set of conditions. Motivated from this standpoint, this paper proposes a model reference adaptive control approach to relax this fundamental stability limit, where an adaptive control signal is augmented with an adaptive robustifying term. The key feature of our framework allows the closed-loop dynamical system to remain stable in the presence of large system uncertainties when the unmodeled dynamics satisfy a set of conditions. An illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.