A Cubic-modification law for robust Model Reference Adaptive Control (MRAC) systems

Robust Deterministic Model Reference Adaptive Control (DMRAC) systems aim at controlling a plant with unknown parameters in the face of disturbances and/or unmodeled dynamics. Our analysis of the dynamics generated by the so-called ??-modification and e1-modification laws has revealed the rich dynamics inherent in such DMRAC systems. The analysis in fact has characterized the causes of undesirable dynamic behavior. Suggested by the analysis, we introduce a new modification law which improves the robustness of adaptive systems and could ensure the convergence to unique (steady-state) erros. Our presentation will motivate the new update law from investigations of a simple prototype adaptive control system with a single unknown pole and an unknown constant disturbance. The analysis is supported with simulation results. We then present the general form of the new update law for n-dimensional DMRAC systems.