Model-Reference Adaptive Control--Stability, Parameter Convergence, and Robustness

We study stability, parameter convergence, and robustness aspectsof single input-single output model-reference adaptive systems.We begin by establishing a framework for studying parametrizableand unparametrizable uncertainty in the plant to be controlled.Using the standard assumptions on the parametrizable part ofthe plant dynamics we rederive a modified proof (of Narendra,Lin, and Valavani) of the stability of the nominal adaptivescheme. Next, we give conditions on the exogenous input to theadaptive loop—the reference signal—to guaranteeexponential parameter and error convergence. Using our frameworkfor studying unmodelled (unparametrized) dynamics; we show howthe model should be chosen, and the update law modified (bya deadzone in the update law) to preserve stability of the adaptiveloop in the presence of output disturbances and unmodelled dynamics.Finally, we compare adaptive and non-adaptive control and listdirections of continuing research.