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

Abstract

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