Adaptive Control of Dynamical Systems with Unstructured Uncertainty and Unmodeled Dynamics

Model reference adaptive control of dynamical systems with unstructured system uncertainties and unmodeled dynamics is considered in this paper. Specifically, a stability tradeoff for this class of dynamical systems is shown first. With the goal of relaxing the resulting stability tradeoff, adaptive robustifying terms are designed next. The key aspect of the proposed relaxation procedure is that the proposed terms guarantee closed-loop system stability even with respect to significant system uncertainties, subject to unmodeled dynamics satisfying a condition. An illustrative numerical example is further given to demonstrate our theoretical findings.