A Direct Uncertainty Minimization Framework in Model Reference Adaptive Control

This paper considers stabilization and command following of uncertain dynamical systems and presents a new adaptive control approach with improved system performance. The proposed framework consists of a novel architecture involving modification terms in the adaptive controller and the update law. Specifically, these terms are activated when the system error between an uncertain dynamical system and a given reference model, which captures a desired closed-loop dynamical system behavior, is nonzero and vanishes as the system reaches its steady-state. This key feature of our framework allows to suppress the effect of system uncertainty on the transient system response through a gradient minimization procedure, and hence, leads to improved system performance. We further show that by automatically adjusting the design parameter of the added terms in response to system variations, we can enforce system error to approximately stay in a priori given, userdefined error performance bounds. Several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.