Fractional-Order Parameter Update Law for Adaptive Control of Integer-Order Systems

This contribution investigates the extension of the certainty equivalence based model reference adaptive control (MRAC) towards fractional-order parameter update laws. We use the infinite state representation of the fractional-order integral for constructing an integer-order Lyapunov function to derive the parameter update law. This renders the model reference error asymptotically stable.In comparison to the integer-order MRAC the fractional-order approach increases the robustness with respect to unstructured uncertainties and allows for higher adaptation rates due to the algebraic type of convergence. All the results are illustrated with a simulation example stabilizing the benchmark of the wing-rock dynamics.