A Discrete Fractional Order Adaptive Law for Parameter Estimation and Adaptive Control

In this article, a discrete fractional order adaptive law (DFOAL) is designed based on the Caputo fractional difference to perform parameter estimation of structured uncertainties. The paper provides a rigorous stability analysis of the DFOAL parameter estimation method. The DFOAL is then modified in order to improve parameter estimator performance to show that, under certain conditions, it provides asymptotic convergence to the true parameter values even when the regressor is not persistently exciting. A method to allow for practical implementation of the DFOAL and the modified DFOAL is developed. Finally, the modified DFOAL is used to identify the plant parameters in an indirect adaptive control law for a class of nonlinear discrete-time systems with structured uncertainty.